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ELEMENTS OF LOGIC; 



DESIGNED AS A 



MANUAL OF INSTRUCTION 



HENRY COPPEE, A. M., 

PROFESSOR OP ENGLISH LITERATURE IN THE UNIVERSITY OF PENNSYLVANIA /iND 

LATE PRINCIPAL-ASSISTANT PROFESSOR OF " ETHICS AND ENGLISH 

STUDIES" IN THE UNITED STATES MILITARY ACADEMY 

AT -WEST POINT. 



PHILADELPHIA: 
PUBLISHED BY E. H. BUTLER & CO. 

1860. 





V 



C7^ 






Entered, according to Act of Congress, in the year 1857, by 

E. II. BUTLER & CO., 

In the Clerk's Office of the District Court of the United States, in and for 
the Eastern District of Pennsylvania. 



Will be published in January, "ELEMENTS OF RHETORIC, 
Designed as a Manual op Instruction," by Henry Coppee, A.M., 
Author of " Elements op Logic." 1 vol. duodecimo. 

In preparation, "ENGLISH WORDS, THEIR ORIGIN, HISTORY, 
SIGNIFICATION AND PROPER USE, Designed as a Manual op 
Instruction," by Henry Coppee, A.M., Author of "Elements op 
Logic," etc., etc. 

LC Control Number 




tmp96 025788 



PEEFACE. 

The following treatise has been written in the hope 
that it may supply, in some degree, a real want. For 
several years the author was a teacher of Logic, in 
the Military Academy at West Point, where the sub- 
ject was thoroughly studied by the aid of Archbishop 
Whately's text-book. 

How much a manual was needed before that ivork 
appeared may be known from the significant fact that, 
as soon as it was published as an article in the Ency- 
clopaedia Metropolitana, it was eagerly caught at 
by the community of teachers, and used, unaltered, 
as a book for college instruction, on both sides of the 
Atlantic. 

Since the publication of that article many have 
attempted the preparation of a manual, which should 
have the instruction of classes as its original design ; 
but the soundness of Whately's views and the con- 

(3) 



IV PREFACE. 

ciseness of his expression, still give to his work the 
greatest circulation. Among so many endeavours the 
author would venture to express the hope that his little 
manual may find its special purpose and mission : it 
is short ; it is explanatory of all the difficult points so 
often left to confuse a student ; the arrangement is 
simple, and much that in a larger treatise would be 
of necessity included, is here omitted, so that what 
the student learns in the limited time of a college 
term, he may learn well, and retain in his memory as 
a basis for further investigations. To some persons 
it may seem too much simplified ; but let it be remem- 
bered that it is a manual for youth ; and that its only 
aim is to teach them the Elements of Logic, as the 
foundation of all reasoning. 

The basis of the work is < Whately's Logic' ; many 
of the examples are taken directly from that ; so many 
indeed, that the acknowledgment is here made for 
them all, and for much that is excellent in arrange- 
ment and in expression. As the clear expounder of 
Aristotle, and the originator of much that is valuable, 
Whately must stand at the head of the Logicians of 
this age. The author would refer specially also to 
the material assistance obtained from " Devey's 



PREFACE. 



Logic,'" (Bolin's series), "Aristotle's Post and Prior 
Analytics" (Bolin's translation); Neil's Art of Rea- 
soning ;" « Blakey' 's Historical Sketch of Logic;" 
" Lord Bacon s New Org anon ; Arnauld (Logique de 
Port Royal); J. Bentharns "Book of Fallacies." 
From Neil a few of the examples have been taken. 

Besides these he has consulted a great number of 
works, the aid derived from which is so general that 
they do not require special mention. 

University of Pennsylvania, July, 1857, 



1* 

% 



NOTE TO THE REVISED EDITION. 

The Author begs to express his thanks for the 
great favour shown this work ; it has been adopted in 
many of the principal colleges and seminaries in the 
country; and he has, in consequence, thoroughly 
revised it, embodying the details of his own expe- 
rience, and the suggestions of practical teachers who 
have used it. The examples for logical praxis at the 
close, form the principal addition to the volume. 

University of Pennsylvania. October 4, 1858. 



TABLE OF CONTENTS. 



CHAPTER I. 

PAGE 

Section 1. Logic; the meaning of the term and the scope of the 

Science 13 

2. Sources of Error . . . . . . . .14 

3. Logic and Philosophy . ; . . 16 

4. Objection to Logic as an Art 19 

5. Natural Logic 21 

6. Systematic forms of Error 22 

7. Of Method 23 

8. Analysis and Synthesis 26 

9. Analysis and Synthesis as applied to Logic . . .30 
Proposed plan of Study: 1. An Analytical View of 

Logic. 2. A Synthesis of Formal Logic. 3. A His- 
torical View of Logic 31-32 

(7) 



Vlll TABLE OF CONTENTS. 

CHAPTER II. 
Analytical View op Logic. 

PAGE 

Section 10. The reasoning process analyzed . . . .33 
The Dictum of Aristotle 36 

CHAPTER III. 

A Synthesis of Logic. 

Section 11. Of certain operations and states of the mind in the pro- 
cess of Argument 40 

1. Apprehension. 2. Judgment, 3. Reasoning or Ra- 
tiocination 41-43 

CHAPTER IV. 

Section 12. Of Terms 45 

13. Division of Simple Terms ...... 47 

14. Quantity and Quality of Terms 49 

CHAPTER V. 

Op those operations in Logic which relate to Terms. 

Section 15. Abstraction and Generalization 51 

16. Species, Genus, and Differentia 52 

17. Property and Accident 53 

18. Of the different orders of Genera and Specie3 . . 56 

19. Realism and Nominalism 58 

20. Definition of Terms 58 

21. Nominal and Real Definitions 62 



TABLE OF CONTENTS. IX 

PAGE 

Section 22. Rules for Definition 63 

23. Division 63 

24. Recapitulation . . 73 



CHAPTER VI. 

Section 25. Propositions 75 

26. Propositions divided into Simple and Compound . . 79 

27. Quantity and Quality of Propositions . . 81 

28. Of the Distribution of Terms in Propositions . . 85 

29. Conversion 8S 

30. Of Opposition 94 

31. Of the Matter of Propositions 96 

32. Of Compound Propositions 99 

33. The New Analytic 103 



C1TAPTER VII. 

Section 34. Of Arguments 106 

35. Of the Syllogism 108 

36. Logical Axioms and Rules 109 



CHAPTER VIII. 
Op Figure and Moods. 

Seetion 37. Figure . . . • 117 

38. Of Mood. Examples 121 

39. Of Reduction 134 



X TABLE OF CONTENTS. 

PAGE 

Section 40. Indirect Eeduction 139 

41. Notation of the Syllogism ...;.. 142 



CHAPTER IX. 

Of Irregular, Informal, and Compound Arguments. 

Section 42. Of Abridged Syllogisms 147 

The Enthymeme 148 

43. The Sorites, or Chain Argument . . . .151 

44. Of the Epichirema 155 

45. Of Hypothetical Syllogisms 157 

Conditional Syllogisms. Disjunctive Syllogisms. The 

Dilemma 158-164 



CHAPTER X. 
Fallacies. 

Section 46. The Meaning and Comprehension of a Fallacy . . 170 

47. Of Fallacies in dictione, or Formal Fallacies . . 172 

48. Material, or Informal Fallacies {extra dictionem) . 175 

49. Verbal Fallacies 188 

I. Etymology. II. Fallacy of Interrogations. III. 

Amphibolous Sentences. Causes of Ambiguity 191-194 

50. The manner of removing Ambiguity in Terms . 201 

51. The Fallacy of Probabilities, or the Calculation of 

Chances 202 

52. Popular Fallacies 205 



TABLE OF CONTENTS. XI 
CHAPTER XL 

PAGE 

Section 53. Of certain modes in which Logic is applied . , 211 

CHAPTER XII. 

A Historical Sketch op Logic. 

page 

Section 54. Division of the Subject 220 

55. Aristotle 222 

56. The Logic of Christianity 236 

57. The Logic of Experimental Philosophy . . . 252 

58. Logic in the Eighteenth and Nineteenth Centuries . 266 

59. Of Categories and Classification .... 268 

60. Conclusion 275 



APPENDIX. 
Examples for Praxis. 



LOGIC 



CHAPTER I. 

LOGIC : THE MEANING OF THE TERM AND THE SCOPE 
OF THE SCIENCE. 

(1) . Of the term Logic. 

As of all the Greek words which have been trans- 
ferred to our English speech, none is vaguer and more 
subtle in its meaning than the word logos (^oyos,) so 
of all the sciences, none is less understood both as to 
its meaning and its scope, than the science of Logic, 
the name of which is taken from that word ; and, in 
consequence, no term is more erroneously applied and 
more frequently misapplied than the name itself. 
As ^oyoj means a word, some writers have sup- 
posed Logic to be simply the science of spoken or 
written words, and have thus confounded it with 
Rhetoric and even with Grammar : others, con- 
sidering a word to imply not simply the written 
or the spoken sound, but also the expres- 
2 (13) 



14 LOGIC. 

sion of the thought, have supposed Logic to be the 
science of thought, and have thus confounded it with 
Intellectual Philosophy, or the investigation of the 
laws of thought and mind : others still, and by far the 
greater number, regarding it as a union of language 
and thought in the deduction of truth, have claimed 
that it had to do with the subject-matter of scientific 
investigation, and have thus erred more widely than 
all by confounding Logic with the labours of physical, 
metaphysical, and ethical philosophy. 

It seems necessary then, at the beginning of a trea- 
tise on this subject, to define the meaning of the word, 
and the true scope of the science, before we under- 
take its study : — to rid ourselves, as it were, of the 
mists which surround us, before we can even see 
clearly the field in which we are to labour. 

(2.) Sources of Error. 

Many accurate thinkers have confused the minds 
of students by producing books, which, while they 
contain a just view of the logical system itself, attempt 
at every step to explain the subject-matter upon which 
this system is employed, and which forms no part of 
it ; while many others, adopting strongly the views of 
those who have initiated so-called systems of logic, 
have, as partisans, carried forward from period to 
period old errors and old perplexities ; and, themselves 
ignorant of the subtleties which surround them, have 



SOURCES OF ERROR. 15 

called their views the true logic, and those of every 
other writer false. Others again have endeavoured, in 
an amiable but unscientific spirit, to harmonize all the 
schemes of the philosophers, and to call the result, 
full of error and inexactness, the system of Logic. 

There are indeed in the systems of the great philo- 
sophers many parts that are mutually dependent, and 
true science will be found to harmonize with itself 
everywhere. But since there is also error in them all, 
no mere greatness of name should exempt from the 
scrutiny and exposure of error. 

We must take care to distinguish between the dif- 
ferent functions of the intellect, so as to call things 
by their right names; not including in the name 
Logic what belongs to Physics or Metaphysics, but 
laying down at the outset the limits and province of 
that system, which we wish to designate by the word 
Logic. If we can do this we shall have accomplished 
very much at the beginning, and shall find our labour 
easy as we proceed. 

If we would see how important it is rightly to 
understand this fact of the ambiguity which the word 
Logic has produced in the minds of men, we need but 
look for a moment at the error into which modern 
philosophers have fallen, when speaking of the Logic 
of Aristotle as compared with the Logic of Bacon. 
If, as we shall endeavour to demonstrate, Logic is 
the science wliicli controls the universal and ultimate 



16 LOGIC. 

principle of reasoning, given to man, just as speech 
was given to him, by a beneficent Creator, then it 
is not Aristotle's Logic, nor Bacon's Logic, but a 
single, universal Logic, given to man as the rule of 
his reason, which must be intelligible and harmonious 
wherever and by whomever it is used. 

(3.) Logic and Philosophy. 

In this consideration another word plays a pro- 
minent part. The word which has been pressed into 
service, to denote the peculiar progress of great 
minds in the domains of Truth, is u Philosophy ;" 
but even the word " Philosopher," adopted by a wise 
ancient* as a more modest title than a o$os, as the 
sages of Greece were called, has been productive of 
great confusion. " Philosophy" has been made to 
stand for a thousand sciences, and to preside in the 
kingdoms of mind, morals, and physics, until to be a 
philosopher means to pursue one of many intellectual 
pursuits, and Philosophy unqualified means every- 
thing or nothing. 

And yet this vague and inexact term Philosophy, 
is the one which has been most frequently confounded 
with Logic, and a want of clear definition and of a just 
understanding in the dispute, has led to the produc- 
tion of abominable, distorted, and monstrous systems, 

* Pythagoras. 



LOGIC AND PHILOSOPHY. IT 

both of Philosophy and Logic, which have confused 
those desirous of learning, and deterred many from 
the difficult and perilous attempt. 

Indeed both words, and the errors to which their 
use has led, indicate, at once, the yearning and the 
weakness of the human mind, — the desire of man to 
investigate and systematize truth, combined with the 
obscurity and doubt which beset his investigations at 
every step. 

The acuteness of the Greeks, upon which had been 
grafted all the power and attainment of the Oriental 
world, could reach no clearer nomenclature, than to 
call their studies and their inductions Philosophy — 
the love rather than the attainment of wisdom ; and 
the art by which they reasoned from truth to truth, 
by which they progressed from parallel to parallel in 
the sea of doubt and uncertainty, Logic, the art of 
words or discourse, the very mention of which sug- 
gests a dubious question, and calls up, as it were, two 
opponents in considering it. 

In avoiding these errors, let us agree to regard 
Philosophy as the investigation of truth, as to its 
subject-matter, the process of finding materials, and 
of classifying and aggregating observations and ex- 
periments, and Logic, as the simple reasoning process 
by which we pass from truth to truth already found, 
and by which we guard against false arguments in 
such a passage. 



18 LOGIC. 

Having thus seen that the name Logic is in a great 
degree arbitrary, and that we should not attain to an 
understanding of the subject, if we followed, even 
remotely, the etymology of the word, we repeat that 
Logic has to do neither with the words themselves — 
except as they are arranged into 'propositions and 
arguments — nor with their meanings, but only with 
the process of reasoning, i. e. passing from tivo known 
and acknowledged judgments to a third which is 
derived from their combination. In general words, 
then, we may state a definition of the term. Logic is 
the Science and the Art of Reasoning. 

Of these two terms, Science and Art, we remark 
that Art is in a critical sense more extensive than 
Science, since the practice of an Art implies the 
application of the principles of Science, while on the 
other hand, Science might, indeed does exist in its 
theoretic state without being put to practical use. 
The Science would be the investigation of the prin- 
ciples upon which the human mind is based in reason- 
ing, and the Art, the application of those principles 
to the establishment of practical rules for conducting 
the process. Logic may then be more simply defined 
the Art of Reasoning, and as such we shall consider 
it in these pages : less concerned about the composi- 
tion of man's reason, than about the practical laws 
and methods by which it works. 

Before proceeding to explain the system of Logic, 



OBJECTION TO LOGIC AS AN ART. 19 

which has developed itself since the days of Aristotle, 
let us meet at the threshold some plausible objections 
which have been brought against the establishment of 
any system whatever. 

(4.) Objection to Logic as an Art. 

As man has been universally gifted with reason by 
means of which he may combine his thoughts and 
arrive at just conclusions, and with language in which 
to communicate them, it is asserted that every man 
carries his own Logic within him, as the immediate 
gift of God. 

All men reason, it is true, and many men are not 
aware of the logical process which they use ; and this 
has been made, even by men of acute minds, an objec- 
tion against Logic ; for, they say, since men reason, 
and reason well, without rules, and without knowing 
the process, a system of rules must be unnecessary. 

The objection is plausible, and has been fruitful of 
evil. But as it is one which may be brought against 
many other arts as well as Logic, it may, we think, 
be most easily met, and most clearly refuted by illus- 
tration. Many children speak with correctness and 
precision before they have any knowledge of Grammar ; 
and there are persons of wonderful powers in arithme- 
tical computation who have never learned Arithmetic ; 
but Grrammar and Arithmetic are not for such reasons 
condemned : their rules are an infallible test for 'pre- 



•20 LOGIC. 

cise speaking, and correct computation, and are thus 
guides to the weaker and slower intellects, — and these 
constitute the immense majority of mankind, — to keep 
them from formal error. So, too, in Music and Paint- 
ing ; great geniuses arise in both Arts, but no one 
would contend that hard study, according to the estab- 
lished systems of the great composers, and the great 
masters — established upon the true principle of voice 
and ear — is not absolutely requisite to excellence 
and success. 

Many persons of clear perceptive faculties, and 
who form and combine their judgments rapidly, may 
reason acutely and well without a system of rules ; 
but, in order to be certain of their correctness, others 
must have some invariable test ; on the other hand 
there are many, of quick but erratic minds, who rea- 
son with such dangerous sophistry that the most deli- 
cate logical tests alone can expose the fallacy, of 
which indeed they may not themselves be entirely 
aware. As such delicate tests have not been within 
the reach of the multitude, it is thus that men have 
become, for want of a popular knowledge of Logic, 
at once self-deceivers and deluders of mankind : have 
established illogical religious creeds, monstrous social 
fallacies, false theories of government, which are im- 
mediately made manifest by the simple application of 
Logic. 

Nay more : since Logic is the one, universal princi- 



NATURAL LOGIC. 21 

pie of Reasoning, applied alike to every branch of 
science Exact or Inductive, it seems much more 
necessary that we should establish full and unerring 
rules for our guidance, and thus be kept, at every 
turn, from the manifold errors which arise from sys- 
tems based upon such objections as those we have 
mentioned. 

(5.) Natural Logic. 

The natural laws which govern the human mind in 
its attempts to reason, have been called by the oppo- 
sers of Logical systems, Natural Logic. We accept 
the name, and are ready to allow that this instinct of 
reason is in the main right, and originally, perfect in 
its kind ; but now, in the fallen condition of man, liable 
to be biassed by prejudice, distorted by passion, or 
insidiously tempted into open error. Thus many men, 
who reason correctly on most subjects, are swayed, 
in one or more, by self-interest, partisanship, fashion, 
predominance of the imagination, and such like 
causes : and thus men of equally clear minds, in the 
main, from the same premises draw different conclu- 
sions, or establish the same conclusion by very differ- 
ent premises. Thus also the same man, at different 
periods of his life, or swayed by various circumstances, 
will reason differently ; and from such causes, it is 
evident that each man's natural Logic is not a sufi> 
cient guide for his reason. 



22 LOGIC. 

Yet still it is from this natural Logic, or rather, 
the concurrence of the right reason of many well 
ordered minds, that the science of Logic has been 
deduced. 

By a systematic observation of such minds, as they 
reason, taking care to remove all causes of error in 
each particular case, we establish rules for the reason, 
and are able to detect, by the application of these 
rules to other cases, every fallacious argument result- 
ing from such causes of error. 

There must have been reason before there could be 
a system of laws to govern it, just as we know there 
was language before Grammar was formed. It was 
to systematize this reason, to methodize this natural 
Logic, and particularly to guard against errors in the 
use of the reasoning powers, that a canon was pre- 
pared, and that a complete science of Logic has been 
formed. 

We have spoken in general terms of the confusion 
and error which have grown out of the misapprehen- 
sion of Logic ; the more special phases of it are those 
resulting from an attempt to systematize these general 
erroneous notions. 

(6.) Systematic Forms of Error. 

By a very common misuse of language, we hear 
such phrases as " mathematical reasoning " "moral 
reasoning ," " syllogistic reasoning '," and "inductive 



OF METHOD. 23 

reasoning ;" which would lead us to suppose that 
instead of one there were many kinds of reasoning. 
This is a fruitful source of error. 

These, so-called, different kinds of reasoning are 
only applications of Logic to different subjects, and 
different habits of thought : the Logic in each is the 
same, the subject-matter alone is different. 

It would seem unnecessary to dAvell upon this point, 
but it has been so commonly misunderstood, and the 
error has been so disseminated by professed writers 
upon Logic, that it must be plainly stated and care- 
fully remembered. 

When we speak, then, of a good mathematician, we 
mean one who is able, most surely and rapidly, to 
apply Logic to the investigations of numbers and 
quantity. When we hear of a great theologian, we 
know that he has amassed much theological learning, 
and has applied Logic to it successfully. So too with 
other sciences. 

In general, in which ever of the myriad fields of 
Nature and mind, ardent votaries may wander ; how- 
ever various the stores they may amass, they must all 
come back with their sheaves to the great measuring- 
centre of Logic, and apply its dicta before they can 
compute or use their gathered gains. 

(7.) Of Method. 
Method is the order and arrangement of facts to \ 



24 LOGIC. 

produce a certain result ; to establish new truth, to 
investigate old, and to explain and teach both. It is 
derived from the Greek nee'oSov, which denotes the 
way through which we arrive at a certain result. 

Whatever steps are taken to make knowledge pro- 
fitable, to reduce theory to practice, and to give clear 
and intelligible ideas of science, constitute Method. 
The extension of the term Method, it is evident, will 
differ according to the subject to which it is applied. 

The methods of investigation differ slightly for the 
different kinds of science, but may generally be 
classified under two heads, Analysis and Synthesis, of 
which the former is generally used in the private in- 
vestigation of truth, and the latter for the purposes 
of instruction. 

The successive stages in the discovery, progress 
and establishment of any science, are three, viz. : 
the descriptive, the inductive (also called the expe- 
rimental), and the deductive or exact stage. 

As soon as, by the description of a science, the 
statement of its present condition, its wants, its un- 
known causes, &c, we have a just representation of 
it, we proceed to observation and experiment, or in- 
duction ; and when by induction, or the laboured 
collection of many particular facts and examples, we 
have established general laws, we may then deduce 
from them any particular fact or facts, which it con- 
cerns us to know. 



ANALYSIS AXD SYNTHESIS. 25 

These stages of investigation belong equally to the 
physical and moral sciences, with the slight difference 
in practice, that the vagueness and complexity in- 
volved in mental, spiritual, and social phenomena, 
which all belong to the moral sciences, require more 
delicate and subtle agencies to trace their laws than 
those of the natural world around us. 

And the sources of experiment are not at all ana- 
logous. Here we are surrounded by apparent contra- 
dictions. The world of nature is changeable and 
shifting, and yet it is palpable to our senses ; the laws 
which govern it are mysterious and inscrutable, and 
yet they are constant ; the moral world which is un- 
changeable and eternal, is vague and obscure, and 
the abstract conclusions to which our inductions lead 
us, positive and incontrovertible as they are, are but 
few and unsatisfactory. 

We shall have occasion to consider the subject of 
Method more in detail hereafter, but at present we 
design to apply it to the consideration of Logic. 

We speak of the Method of a single science, or a 
Method which is applied to all — as in that which 
leads to the Classification of the sciences. In either 
investigation the division of Method into Analysis 
and Synthesis, is a just one, as both are used in 
either process. 
3 



26 LOGIC. 



rf" 



(8.) Analysis and Synthesis. 



To illustrate more clearly the nature of these two 
processes, let us take a familiar example. If we 
designed to teach a person how to make and use some 
complicated structure, as, for example, a ship, and if 
this person had never seen one, the first step in the. 
process would be to show him the ship completely 
built and ready to proceed to sea ; fully rigged, 
equipped and manned ; that he might take in at a 
glance its finished appearance, and its ultimate design 
and use : in a word, that he might know what he was 
to learn to make. This would be the first lesson in 
ship-building. The next step would be to show it to 
him partially dismantled, or in effect, to take it to 
pieces before his eyes, that he might see the parts of 
which it is composed, and their relative position in 
the structure. 

The third step would be to show him how each part 
was made, and to let him see them all in minute 
detail lying together, according to some system, which 
should be preparatory to a reconstruction of the 
ship. 

This process of successive steps is Analysis,* or a 
dissolution of anything into its elements. 

In the investigation of any science, it is of primary 



* ai>a\.w — to separate into elements. 



ANALYSIS AND SYNTHESIS. 27 

importance. Showing us at first the scope and design 
of the science, by systematic degrees it decomposes 
it into its elements, and prepares us for intelligent 
study of its many forms. 

This operation shows us also the simplicity of science, 
and is evidently derived from the teachings of nature ; 
for while there are innumerable forms of animal and 
vegetable life, the analysis of nature which is con- 
stantly going on, shows but few parts or elements in 
all her works, and great simplicity of combination of 
the same elements in different proportions, to produce 
the most dissimilar forms and results. So all the 
sciences, physical, intellectual, and moral, while they 
assume many and varying forms, are in reality com- 
posed of a few simple elements of nature or mind, and 
this their analysis displays. 

The analysis of physical science is of course the 
most exact of these processes, in proportion as the 
things of sense are easier to comprehend and fix than 
those of mind and spirit : in physics, this process of 
analysis is carried from the grandest class, such as 
kingdoms and high genera, to the observation and use 
of atoms and molecules inconceivably small, which 
are to constitute the basis-elements of a reconstruct- 
ing process. Accurate analysis is a work of patient 
labour. Chance experiments have indeed occasionally 
produced great results, but this is an argument for, 
rather than against, careful analysis. Roger Bacon dis- 



28 logic. 

covered a fulminating powder when he was not seek- 
ing it ; but, to be useful, this powder must cease to be 
a chance discovery ; that is, it must be analyzed into 
nitre, charcoal, and brimstone, so that, these constit- 
uents once known, we can make our fulminating 
powder at will. Science has never proceeded upon 
chance ; it moves safely only when it moves by in- 
variable but ever-extending laws. 

Incomplete analysis has done more to establish and 
perpetuate error, than even blind superstition. For 
it was in the face of the latter that Copernicus and 
Galileo established the true theory of the heliocentric 
system ; while before their time, the incomplete, 
false, and arbitrary analysis of astronomy, and the 
belief in stellar influences, which a just analysis would 
have destroyed, led all the writers, from the time 
of Ptolemy, to build a false system of celestial 
mechanics ; and thus to clog the wheels of true 
science. 

The process of analysis having been completed, we 
come naturally to Synthesis.* 

Having taken to pieces, we proceed to the other 
task of rebuilding : carefully examining each different 
clement as they all lie before us, until we understand 
thoroughly the material of which it is made and its 
construction, we proceed to adjust it to its place in 
the structure : piece by piece, perhaps slowly and pain- 



'riO-ifit — to place together. 



ANALYSIS AND SYNTHESIS. 2i) 

fully, we build the ship, until at length it is complete : 
nor is the labour yet finished ; we launch it upon the 
waters, spread its sails to the wind, and see it in 
practical and successful movement, and then we may 
account ourselves acquainted with the structure, and 
able to build its like whenever called upon to do so. 

This operation is called Synthesis ; it is evident 
that it is also continually going on in nature in the 
reproduction out of crude materials of the many forms 
of complicated existence. 

Many writers, in investigating a science, begin with 
this latter process, entirely neglecting the former ; but 
it is so evident that the analysis of a science gives 
large and valuable lessons preparatory to its synthesis, 
or real study for ourselves, that most modern treatises 
on science have adopted and followed this order of 
instruction. It may then be safely stated that in any 
science the true synthesis can only be proportional to 
a vigorous and just analysis, and there have conse- 
quently been rules laid down for proceeding to con- 
sider any science or art in pursuance of this method. 

The rules for Analysis may be reduced to these : — 

1st. Not to believe any general scientific statement 
without proof: that proof determined by the just 
principles of evidence. 

2d. To divide every scientific dictum into as many 
parts or elements as shall be necessary to resolve it. 

3d. To make a methodical arrangement of these 
8* 



80 LOGIC. 

elements in order that we may understand them 
clearly and the relation which they bear to each other. 

Having done this, the corresponding rules for Syn- 
thesis are : — 

1st. To use such terms to express the elementary 
parts as are free from ambiguity. 

2d. In combining these, to assume only such clear 
principles or axioms as cannot be contested by any 
persons. 

3d. To prove, by demonstration, all the conclusions 
at which we arrive, in the employment of the terms 
and axioms used. 

These remarks upon analysis and synthesis, as the 
two vital functions of Method in investigation, and as 
the two necessary instruments of all scientific study, 
are designed for general application. A proper and 
constant application of the rules of analysis and syn- 
thesis would cause great advancement in our studies, 
and would go far to insure us from error, however 
rapid that advancement might be. But we have 
placed the subject of Method in this place, because 
we design to use it in application to the study of Logic 
itself; for, as a science to be studied, Logic comes 
under the rules which have been just laid down. 

(9.) Analysis and Synthesis as applied to Logic. 

Now, let us employ this method in investigating the 
science of Logic. 



PROPOSED PLAN OF STUDY. 31 

That we may study the subject profitably, making 
each step a preliminary to the due understanding of 
the successive steps, we propose to divide the entire 
subject into the following special considerations : — 

1. AN ANALYTICAL VIEW OF LOGIC. 

In this we regard the science in its aim and its 
workings, and after thus showing its design and its 
scope, we analyze or dissolve it into its different parts, 
showing what those parts are which effect by their 
combination the purpose designed. 

2. A SYNTHESIS OF FORMAL LOGIC. 

As Synthesis is the reverse process of Analysis, and 
as an Analysis of such a study would be in reality 
but a general view of the scope of that science which 
Synthesis is to establish, we shall see that while our 
analytical view of Logic may be brief and general, our 
synthesis must be minute and careful. We must more 
particularly examine those parts which our analysis 
has given us, in order that we may be able duly to 
combine them in their just relations. 

In imparting instruction upon subjects which are 
known, the synthesis is evidently the more important 
process, and hence must be longer and more minute ; 
while in the investigations of an unknown science the 
analysis is the more important and valuable process. 



5Z LOGIC. 

In the general synthesis of Logic we shall also 
devote a chapter to the subject of Fallacies ; and 
then consider some of the ways in which the syllo- 
gism is used, and the technical phrases which ex- 
press these uses. 

3. A HISTORICAL VIEW OF LOGIC. 

This historical view of Logic has been placed after 
the study of the formal Logic, rather than before it, 
as is usual in most treatises, because we can appreciate 
a history only of that which we know, and we shall 
understand much better the causes of error and the 
obstacles to science which history gives us, when we 
are beforehand aware of the true scope and relations 
of the particular science whose history is related. 
When we know what Logic is, its history is intelligible 
and interesting, and not otherwise. 

For Logic is so intermingled or rather entangled 
with other kinds of philosophy in almost all of its 
principal epochs, that any one who should undertake 
to read of its adventures in history without being 
able constantly to dissociate it from its companion 
sciences, would find it a useless and unprofitable task. 



ANALYTICAL VIEW OF LOGIC. 33 

CHAPTER II. 

ANALYTICAL VIEW OF LOGIC. 

(10). The reasoning process analyzed. 

To apply the method of analysis to the study of 
Logic as an art, we begin with the definition already 
laid down that Logic is the Art of Reasoning. 

Reasoning consists in the combination of two known 
judgments to form a third, which is deduced from 
them. Reasoning, when expressed in language, is 
called argument. 

The ultimate and simple form of argument, logi- 
cally expressed, is the syllogism* In a more extended 
sense, reasoning covers also the combination and suc- 
cession of many arguments. 

The syllogism is an argument consisting of three 
propositions, of which the first is called the major pre- 
miss, the second, the minor premiss, and the third, 
the conclusion. This is the usual order of the pre- 
misses, but the reasoning would be equally valid, 
were they transposed. 

Major premiss. All A is B = All men are mortal. 
Minor premiss. All C is A = All Hindoos are men. 
Conclusion. Therefore all C is B = All Hindoos are mortal. 



* avv and \oyit,onai, more remotely Xsyw. 
C 



\ 
34 LOGIC. 

Each of these propositions consists of two terms, 
the subject and the predicate ; and the verb uniting 
them is called the copula. Men reason to satisfy 
their own minds, to convey instruction, or to refut< 
error, and in so doing, they combine many of these 
syllogisms, thus forming compound arguments, which 
may always be analyzed into the simple arguments 
which compose them. In a simple syllogism, in many 
cases, one or other of these premisses conveys a fact 
so well known that it may be taken for granted, and 
so it is suppressed, and thus is formed an abridged 
argument, called an enthymeme. For example : — 

(Minor premiss.) Csesar -was a man, 
Therefore Caesar was mortal. 

This is an enthymeme with the major premiss 
suppressed. This major premiss is, All men are 
mortal, which is taken for granted in the conclusion, 
where, because Cwsar was a man, it is affirmed that 
he was mortal. In every case, however, if the enthy- 
meme appear at all doubtful, the suppressed premiss 
may be written out, and the validity or invalidity of 
the argument thus determined. Compound argu- 
ments, instead of having each syllogism fully ex- 
pressed, are usually formed of a number of enthymemes 
combined. 

The groundwork of the syllogism is the dictum of 
Aristotle, or his universal test for Argument. 

Without in this place entering even very briefly 



Aristotle's dictum. 35 

into the History of Logic — a history of experiment 
and error — it is interesting to know the time of its 
first decided manifestation, and the person to whom 
we owe it as a definite science. In that magnificent 
period when the school of Plato had prepared the 
mind of Greece for the coming of Aristotle, and the 
energy of Philip had opened the way for the con- 
quests of Alexander, that system of Logic was 
formed, which, after having passed through the 
fiercest ordeals, has remained almost without change 
to our day. It has been indeed covered up, and to 
all appearance lost, in the times of European bigotry 
and ignorance ; schoolmen and churchmen have alike 
assailed it ; but with the vital principle of truth, it 
has remained untouched by the ruinous hand of 
Time, amid exploded systems of Ethics, false specu- 
lations of Philosophy, and the cunning allegories 
of Heathen mythology. The Analytics of Aristotle 
form the cyclopaedia of Logic in this age, as in all 
former periods. 

After many years of patient investigation Aristotle 
established the "Dictum de omni et nullo," of which 
the first part, de omni, refers to all affirmative reason- 
ing, and the second, de nullo, to all negative reason- 
ing. Stated by the use of ordinary symbols it would 
be written as follows : — 

j * 



36 LOGIC. 

The Dictum of Aristotle. 



De omni. 


De nullo. 


All A. is B. 


No A. is B. 


(1) (2) 


(1) (2) 


All or some C. is A. 


All or some C. is A, 


(1) (2) 


(1) 



Therefore all or some C. is B. Therefore no C. is B., or some C. 

(2) 
is not B. 

Or if stated by a geometrical notation, as all syllo- 
gisms may be stated :- 



(1) _ (2) 

/ 

B [ A 




§)0 €3© 



But to explain the dictum practically, it has been 
translated thus : — 

Whatever may he predicated of a whole class, may 
also be predicated of all or any of the individuals con- 
tained in that class. 

To predicate* means to affirm or deny. 

Thus in the dictum de omni. In the major premiss 
we predicate or affirm B. of the whole class A. 

In the minor premiss we assert that all or some C. 
is an individual or a number of individuals included 
under the class A. : 

And in the conclusion we predicate B. of the indi- 
viduals, as we did in the major premiss of the whole 
class to which they belong. 

This simple dictum of Aristotle is the groundwork 
of the syllogism, and the syllogism is the universal 

*Prcvdko — are, not prcdico — cere. 



THE DICTUM OF ARISTOTLE. 37 

principle of reasoning. It is sufficient in this place 
to state the fact ; it will be proven hereafter. The 
propositions of which the syllogism is composed are 
further analyzed. A proposition consists of two terms 
and a copula, of which the first term is called the sub- 
ject, the last the predicate, and the connexion between 
them is the copula. 

subj. cop. predic. 

(men) (are) (mortal). 
subj. cop. pred. 

(men) (are not) (trees.) 

It has been said that the dictum of Aristotle is the 
groundwork of the syllogism, and that the syllogism 
is the universal principle of reasoning : it must be also 
remarked that every valid argument, no matter what 
may be its original form, may be put under the form 
of the syllogism, and to it in that form the dictum may 
be directly applied ; and, on the other hand, if any 
argument cannot be reduced to this form, it is invalid. 
Thus this dictum forms not only the vehicle of correct 
reasoning, but is a sure test of error in Logic. We shall 
constantly recur, in considering every form of argu- 
ment, to this test. 

The reasons why in mathematical investigation we 
use letters, and in arithmetic numbers, are ; — first, to 
expedite and simplify the work, and secondly, to gene- 
ralize it. For the same purposes we use symbols in 
Logic. If, for example, I write the syllogism 



38 LOGIC. 

All good men are happy, 
John is a good man, 
Therefore, John is happy ; 

I limit my argument entirely to the particular of John 
being a good man and being happy, whereas, if I write 

All A. is B., 

C. is A., 

Therefore C. is B. ; 

I propose a general formula which will apply to 
many cases according to the subject and the matter 
of inquiry. It will be well for the student to frame 
particular examples under the general formula, and 
thus at once to fix the form in the mind and accustom 
himself to the practical applications of the system 
of Logic to particular cases. 

Besides the dictum of Aristotle, to the form of which 
every valid argument may be reduced, there will be 
given hereafter a series of rules for detecting fallacy 
and for determining the validity of an argument when 
it is not exactly in this form, and, by means of these, 
the logical student may defend himself against the 
subtlest sophistry, holding Aristotle's dictum in re- 
serve as a final test. Where one who is ignorant of 
Logic is obliged to use much effort and circumlocution 
to determine the validity or invalidity of an argu- 
ment, and is in great danger of error in the process, 
the logician, at once and without inquiry into the 
subject-matter of discourse, applies his tests to the 



THE DICTUM OF ARISTOTLE. 39 

framework of the reasoning, and indicates infallibly 
the defect in the argument. And so deciding as to 
the validity or invalidity of the general formula as 
expressed by the symbolical letters A., B., C, he has 
once for all decided for each particular example which 
can fall under that formula. 

In concluding this brief analysis of Logic, let us 
recapitulate. Logic is the Art of Reasoning : there 
is but a single universal principle of Reasoning : its 
basis is the dictum of Aristotle, and its simple form 
is the syllogism. 

The syllogism is composed of two premisses and a 
conclusion : each of these is a proposition ; and each 
proposition consists of three parts, two terms and a 
copula. It is now our purpose to examine these con- 
stituents of Logical formulae in the inverse order, 
beginning with terms. 

o — ^ 



4J LOGIC. 



CHAPTER III. 

A SYNTHESIS OF LOGIC. 

(11.) Of certain operations and states of the 
mind in the process of Argument. 

In proceeding to the synthesis of the reasoning 
process, we must first consider certain operations and 
states through which the mind passes in approaching 
an argument. Logicians have enumerated many 
which are so nearly related to each other, that we 
may reduce them to three. 

These are : 1st. Apprehension ; 2d. Judgment ; 
3d. Reasoning, or Ratiocination. As a preparation 
for these in their order, Attention has been called the 
primary state : hut this is self-evident. Apprehension 
is a pure mental consciousness of the existence of an 
object arising from perception ; perception being the 
process of conveying an impression to the mind, 
through the senses. We must first perceive an object 
before we can apprehend it. 

By the five senses of the body we have a know- 
ledge of the world around us ; the first step in obtain- 
ing this knowledge, is sensation, or the impression on 



A SYNTHESIS OF LOGIC. 41 

the organ of sense; sensation is conveyed in a myste- 
rious, inexplicable manner to the mind, to produce 
perception ; and as soon as we have perceived the 
object by this union between the mind and the senses, 
apprehension or an intelligent knowledge of it is 
produced. 

Apprehension is simple or complex. 

Simple Apprehension is the notion of one object or 
of several which bear no relation to each other ; and 
this notion is expressed generally by one word, as 
John, man, river ; or by many connected by conjunc- 
tions, John and Peter ; the man and the hoy. 

Complex apprehension is the notion we form of 
several objects which bear a relation to each other, 
as a man walking, a bundle of rods. 

When an act of Apprehension is expressed in lan- 
guage, it is called a term. 

But, whereas certain words, which express terms, 
are equivocal or ambiguous, it must be observed that 
Logic deals only with general or abstract terms, and 
has nothing to do with their distinctness or indistinct- 
ness. It only takes for granted that a term is dis- 
tinct and unambiguous. A Logical term then is a 
simple, unequivocal act of apprehension, expressed in 
language. 

2. Judgment. 

Judgment is that operation of the mind, by which, 
if we have two objects of apprehension or terms, both 
known to us, we declare that they agree or disagree 



42 LOGIC. 

with each other. Thus, if I know who "John" is, 
and what " a her •(?" is, — I may declare that — 

John is a hero. 
Or that — John is not a hero. 

Judgment is therefore of two kinds, affirmative 
when the two terms are declared to agree; and nega- 
tive, when they are declared to disagree. 

An act of Judgment when expressed in language, 
is called a proposition. 

And here, also, it must be observed, that Logic 
only takes cognisance of abstract propositions, which 
are expressed by logical formulae, and has nothing 
to do with their truth or falsity. It takes for 
granted indeed, that, when a proposition is stated, it 
is true. 

For example, if the proposition be A. is B. it is 
assumed by Logic, that A. is in reality B. y and thus, 
if, when this general formula be translated into a par- 
ticular proposition, it prove to be false, Logic is not 
responsible for the falsehood, nor for the error which 
finds its way into an argument by reason of the use of 
a false premiss. Much error has arisen through the 
mistake of supposing that Logic had to do with Lan- 
guage directly, and with the judgments expressed in 
language ; but it is just such an error as would lead 
us to assign such values to the unknown quantities in 
any algebraic formula, such for instance as y 2 — 2px 
=== 0, as would destroy the equation. Algebra pre- 



OPERATIONS OF THE MIND IN REASONING. 43 

supposes the equation to be just, and develops only 
such values of x and y as will establish it. The 
Logical formula is as abstract and general as this, 
and Logical propositions are always assumed as true. 

3. Ratiocination. 

Ratiocination is that act of the mind by which, 
having two or more acts of judgment, or propositions, 
we pass to another or others founded upon them and 
growing out of their combination. 

Thus if we have the two propositions 

All men are mortal, 
Gcesar was a man, 

we have, as an inference or fact implied in these two 
propositions, and deduced from their combination, the 
final proposition, Ccesar was mortal. 

An act of ratiocination when expressed in lan- 
guage is called an argument ; and an argument when 
reduced to its simple logical form is called a syllogism. 
That simple logical form demands a certain order in 
the premisses and the conclusion. 

If now we examine the syllogism 

3Iajor premiss. A is B = Men are mortal. 
Minor premiss. C is A = Csesar is a man. 
Conclusion. C is B = Csesar is mortal. 

we shall perceive that it consists of three propositions, 
which are called the major and minor premisses and 
the conclusion ; and three terms represented by A., 



44 LOGIC. 

B., and C, each term being used twice in the syllo- 
gism. The term which occurs in the major premiss 
and the conclusion, (B.) is called the major term ; that 
which occurs in the minor premiss and the conclusion, 
(C.) the minor term, and that which is found in both 
premisses (A.) the middle term. The major term is 
always the predicate of the conclusion, and the minor 
term the subject. 

Extended Ratiocination is conducted by the com- 
bination of many of these syllogisms, or their conclu- 
sions, according to Logical laws. 



OF TERMS. 45 



CHAPTER IV. 

(12.) Of Terms. 

A term has been defined an act of apprehension 
expressed in language, and may be either simple or 
complex. 

A simple term is the name of a single object of 
apprehension, and is generally expressed by one ivord, 
as man, house, field. 

A complex term is the expression of several objects 
of apprehension with the relation which they sustain 
to each other, as a good hoy, a horse running. 

It is evident that the name of a term is arbitrary, 
and of use only to convey the apprehension to another, 
as in different languages the terms which express the 
same object of apprehension will be different words ; 
thus we have the object we call horse, expressed in 
French by the word cheval, and in Spanish by the 
word cabdllo. "Words then, it must be remembered, are 
not terms, but are arbitrary signs for conveying and 
using terms. 

But language, or the use of words, is necessary 



46 LOGIC. 

to the form of reasoning, as no reasoning can be ap- | 
plied and tested until it assumes the dress of language, j 

When a word is capable of being used alone as a , 
term, it is said to be Categorematic,* and when it needs 
the assistance of other words to constitute with it a 
term, it is called Syncategorematic. Thus man, horse, 
John, are categorematic words : here, gave, and, are j 
syncategorematic. 

By a casual examination of the different parts of 
speech we shall find : — 

1st. Of the noun : That it is only categorematic 
when in the nominative case ; the possessive man's 
requires another word denoting the thing possessed, 
and the objective a word which governs it. 

2d. Of the adjective : That it is syncategorematic ; 
for, although we say John is good, we understand 
man or boy after good. 

3d. Of the verb : That it is, so to speak, more than 
categorematic, since it contains often the copula and 
the predicate: as, the man walks; in this sentence 
walks is equivalent to is walking, in which is is the 
copula, and walking the predicate. 

The infinitive mood is often in reality not a verb, 
but a noun in the nominative case. Thus the sen- 
tence To die for one's country is happiness ; means 
Death for one's country is happiness ; To die being 
fully expressed by Death. 

* Karr]y6prijxa = something alleged or affirmed. 



OF TERMS. 47 

4th. Of the remaining parts of speech we see at a 
glance that they are syncategorematic, and are only 
used in connexion with other words to constitute 
terms. The word which has the form of the present 
participle is sometimes an infinitive, and sometimes a 
noun; we might substitute it in the last example 
given as a case of either. Dying for one's country is 
happiness, is equivalent to both the forms given. 

(13.) Division of Simple Terms. 

Simple terms are divided into singular and common. 

A singular term is that which expresses a single 
individual, and is usually the name of a person, place, 
or thing ; as John, Philadelphia, the Delaware. 

A common term is that which expresses any indivi- 
dual or individuals of a whole class ; as a man, the men, 
an army. To make a common term singular, we prefix 
the demonstrative pronoun this or that, as this man, 
that river, which is equivalent to stating the name of 
the man or river ; as, This man is John ; That river is 
the Delaware. Common terms stand for classes, and 
are sometimes called appellative, as giving name or 
appellation to many individuals. 

They thus are of great aid to science, in that, when 
many common properties have been discovered in a 
great number of individuals, and their distinctive 
peculiarities have been discarded, they may all be 
called by one name, and that name will be a common 



48 LOGIC. 

term ; when this is in view a common term is called, 
according to its comprehension, genus or species. 

Common terms are further distinguished accord- 
ing to their matter, into abstract and concrete. 

An abstract term is an ideal word, expressing an 
abstract property capable of inherence in an object, 
and yet without reference to that object. Thus hard- 
ness, length, beauty, are abstract terms, which inhere 
in many objects, but do not indicate any particular 
one. 

A concrete term is one which presents to the mind, 
at once, the property and the existence of the object 
in which it inheres. Thus hard, long, beautiful, are 
concrete terms, implying certain objects which are 
hard, long, or beautiful. 

Concrete terms are also called denotative and con- 
notative, because they denote the abstract property, 
while they connote or imply in their signification the 
body or object to which it belongs. Thus hardness, 
being an abstract term, is also an ideal noun ; the 
mind rests upon the vague idea, because it indicates 
nothing farther ; but when hard is mentioned we feel 
the right to ask, what is hard ? the answer is — stone. 
Thus the concrete term hard has denoted the quality 
of hardness, and connoted stone as the object in which 
that quality inheres. 



OF TERMS. 49 

(14.) Quality and Quantity of Terms. 

Terms are further divided according to their quan- 
tity and quality. 

The quality of a term is the mode or manner in 
which it expresses an act of apprehension. 

Terms are said to be synonymous under this divi- 
sion, when they express the same act of apprehension ; 
but by common usage this exact meaning is departed 
from, and synonymous terms now mean those which 
express different shades of meaning ; thus happiness 
&&([ felicity are synonymous terms, and yet their ety- 
mology teaches us a difference in their meanings ; 
the former attributing pleasure to luck or fortune, 
and the latter simply asserting a state of unalloyed 
pleasure. 

Incompatible terms are those which cannot be used 
as predicates of the same subject at the same time : 
thus hot and cold ; asleep and awake. 

Positive terms are those which state the real exist- 
ence of the objects they stand for. The opposite of 
these are negative terms, or those which deny the 
existence, or assert the absence of certain objects or 
attributes. 

There is a class of terms called Privative, which 
are often confounded with negative terms ; but there 
is a real and important difference between them. A 
'privative term expresses, that some quality or attri- 
bute usually belonging to the class, is wanting in some 
5 ^ D 






50 LOGIC. 

individuals of that class : thus dumb, idiotic, are pri- 
vative terms, since their very names call to the mind 
the fact that man generally is gifted with speech and 
reason. 

Terms are divided according to their quantity into 
many distinct classes, expressing their number and 
dimensions. 

Thus we have the common division of numeral and 
ordinal, as twenty, a hundred, two ; positive (in its 
grammatical sense), comparative and superlative terms, 
as good, better, best. 

That which is more truly a logical division into 
distributed and undistributed: a distributed term 
being one the whole of which is considered, and an 
undistributed term one in which only a part is taken, 
this part being usually an indefinite part, expressed 
by such words as some, few, several, &c. All men is 
a distributed term, some men, an undistributed term. 



OF TERMS. 51 



CHAPTER V. 

OF THOSE OPERATIONS IN LOGIC WHICH RELATE TO 
TERMS. 

(15.) Abstraction and Generalization. 

Abstraction consists in draiving off and consider- 
ing one or more of the properties of an object to the 
exclusion of the rest. Thus we use abstraction when 
we observe the colour and odour of the rose, disregard- 
ing its other characteristics. If we abstract the 
colour and odour of one rose, then of another, and so 
of many, and finding these alike for all, call them all 
by one common name Hose, we are said to generalize. 

Generalization then consists in disregarding the 
differences between many objects which are alike in 
certain properties, and calling them by a common 
name, by reason of their resemblance or identity in 
these properties. 

We may abstract, it is evident, without performing 
the other process of generalizing, but we cannot 
generalize without first abstracting : in the general 
case, however, we abstract for the purpose of gene- 
ralizing. It is by these two processes that we obtain 
common terms, or the names of classes. All these 



52 LOGIC. 

common terms are the result of higher or lower pro- 
cesses of generalization. Thus, by a low generaliza- 
tion, we obtain tea-rose, by a higher, rose, by a higher 
still, flower, and by one step farther, vegetable, &c. 
But common terms, as classes, are further dis- 
tinguished into species and genera ; and, as expressive 
of certain things belonging to the species and genus, 
they are also divided into the differentia, property, 
and accident. Some writers, in considering the sub- 
stance of a term, have called the object for which it 
stands, the essential part or the essence. 

(16.) Species, Genus, and Differentia. 

A species is a class obtained by generalization, 
which includes only individuals or subordinate classes, 
and is itself included in a genus : as an Arabian horse 
is a species of horse; horse is a species of quadruped ; 
quadruped is a species of animal. A genus is a class 
obtained by a higher generalization, which compre- 
hends under it two or more species ; as animal is the 
genus alike of quadruped and biped, quadruped is the 
genus of horse, cow, deer, &c, and biped the genus of 
man, &c. 

It is evident that in one sense the species implies 
more than the genus ; as, for instance, if quadruped 
be the genus and horse the species, horse will contain 
all the signification of quadruped, and also the dis- 



OPERATIONS WHICH RELATE TO TERMS. 53 

| tinctive signification of horse as to shape, size, habits, 
uses, &c. ; which latter does not belong to quadruped. 
For this reason the species is said to express the 
whole essence of the object, while the genus expresses 
only a part of the essence, and that the material part. 
Thus, man expresses the whole or complete essence 
of the animal so called, while animal expresses only 
the comprehensive or material part of the essence 
which only limits him to an animate existence. 

The differentia of an object is the formal or dis- 
tinguishing part of that object, and divides it from a 
class to which it does not belong ; and, when united 
with the genus or material part, forms with it the 
species or whole essence. Thus, if man be the species, 
and animal the genus, rational would be the differ- 

(species) (differentia) (genus) 

entia, and we should have man = rational animal. 
By which it appears that although the genus compre- 
hends this species and many others, the species really 
implies, although in a different sense, more than the 
genus, viz., the genus and differentia. 

(17.) Property and Accident. 
Thus, having shown the relations between the spe- 
cies, or the whole essence, the genus, and the diffei- 
entia, — parts of the essence, — each of which is ex- 
pressed by a common term, we come to consider 
those things which are or may be joined to the spe- 
cies or essence. They are divided as follows : — 
5* 



54 LOGIC. 

I. Property, which is joined universally to the 
essence, and thus must be asserted as belonging to 
every individual of the species ; and 2d. Accident, 
which is joined only contingently, that is, to one indi- 
vidual or certain individuals of the species, and not to 
the whole species. 

Property is of two kinds. 1st. That which is uni- 
versal, or belonging to every individual of the species, 
but not peculiar to the species, as respiration, which, 
although it belongs to all men, is not confined to the 
species man. 2d. That which is universal and pecu- 
liar, as the power of intelligent speech, which, while 
man, as a species, possesses it, is peculiar to man. 
Some writers have erred in enumerating a third kind, 
viz. : peculiar but not universal, as, for example, to 
be able to be a poet. But this violates our definition, 
since, if it belong to some individuals and not to the 
species, it ceases to be a property, and becomes an 
accident. 

II. Accident is something joined contingently to the 
species, or belonging only to certain individuals of it. 

Accident is of two kinds : separable and inseparable. 
A separable accident is a circumstance which may be 
detached from the individual, without affecting his 
identity or altering our general conception of him ; as 
John is walking, or is lying dozen ; in which examples 
the accidental circumstance of walking or lying down 
is not a necessary part of the individual, but may be 



OPERATIONS WHICH RELATE TO TERMS. 55 

detached from him, so that we may still conceive of 
him as doing neither. 

An inseparable accident is one which cannot be 
detached from the individual; as, born in Phila- 
delphia ; born in 1800. 

It is by means of such inseparable accidents that 
a man is described or his history written ; but it must 
be remarked that this phraseology is rather conve- 
nient than exact, for, as soon as the event which we 
call a separable accident occurs in the life of an indi- 
vidual, it really becomes inseparable. Thus, if John 
walked to the city on a certain day, or, being unwell 
afterwards, was lying down in consequence, we can 
no more detach these facts from his history, than we 
can the event of his being born in a certain place, and 
at a certain time. 

Having now illustrated the meanings of genus, spe- 
cies, essence, differentia, property, and accident, let 
us, for convenience and clearness of illustration, write 
out a sentence embodying all these uses of common 
terms, as a model, by which the student will easily 
frame other examples for himself. This sentence will 
also embody the different processes of generalization. 

(property, universal 
(Individual) (species) (differentia) (genus) but not peculiar) 

John is a Man, — a rational animal, who breathes, 

(property universal and peculiar) (separable accident) 

has the faculty of speech, is lying on the sofa, and was 

(inseparable accident) 

bom in Philadelphia. 



56 LOGIC. 

The logical name given to every common term re- 
presenting a genus, species, differentia, property, acci- 
dent, is predicable ; viz., something which may he pre- 
dicated : no other terms than these are predicable. 

(18.) Of the different orders of Genera and 

Species. 

A summum genus or highest genus is the highest 
class of all, and has no genus above it. 

A term which expresses at once a genus and a species 
is called a subaltern genus and species. For example, 
quadruped is a genus of horse and a species of animal. 

In the descending scale from the summum genus, the 
successive or inferior genus is called a subaltern genus. 

In the ascending scale from the lowest species, it is 
called the subaltern species. 

When a genus is divided into its species they are 
called co-ordinate or cognate species, to indicate 
that they are not subordinate to each other. Thus 
if quadruped be divided into horse, cow, lion, as re- 
presenting the equine, feline, and vaccine races, these 
would be cognate species. 

A species which contains beneath it no other species, 
but only individuals, is called an infima or lowest spe- 
cies. In any scientific investigation, however, ranging 
between any two limits although not absolutely the 
highest and lowest, it is usual for convenience to call 
the highest limit named, summum genus, and the low- 
est, infima species ; as though we should say " Let 



OPERATIONS WHICH RELATE TO TERMS. 57 

A be the summum genus, and C the infima species, 
during this investigation." There are also in common 
use the phrases proximum genus and remote genus, 
the first of which means the genus next above, and the 
second, a genus farther removed from, the species in 
question. Thus quadruped is the proximum, and 
animal the remote genus of horse. It is necessary 
that the proximum genus should be the genus next 
above the species in question ; but the remote genus may 
be any one farther removed, and not necessarily the 
summum genus, which is of course the most remote. 

It must be observed that the use of a common term, 
as either species, genus, differentia, property, or acci- 
dent, is a relative use ; and because it is used with one 
of these significations in one sentence, this does not 
deter us from using it with quite another meaning, on 
another occasion. Thus if we take the word red, we 
shall find we can make it serve as each, in turn. 

The colour Red is a genus under which as species 
are ranged pink, scarlet, crimson, vermillion, &c, the 
different kinds of Red. 

Red is a species of the genus colour, and ranges 
with white, blue, yellow, &c, as cognate species. 

Red is a differentia of the " Red rose," which dis- 
tinguishes it from other roses. Red is a property of 
blood ; and an accident of a house, separable if it be 
painted red, inseparable if it be built of Red stone. 
And thus in analyzing any sentence we must be care- 



58 LOGIC. 

ful to ascertain the real value of the common terms 
employed. 

(19.) Realism and Nominalism. 

"While upon the subject of common terms, it is well 
to refer to the long-standing controversy between the 
Realists and the Nominalists, which, although it became 
strangely intermixed with theology and church polity, 
had its origin in the significance of a common term. 
It will be referred to more at length in the historical 
view. The Realists contended that every common terra 
was the name of something really existing ; that a 
genus and a species were real things, while the Nomi- 
nalists believed that we obtained common terms merely 
to express a certain inadequate undefined notion of 
one individual, which we apply to many. 

It would seem to be a trivial subject for controversy, 
but the more we examine it, the more difficult and 
subtle it appears. Like many subtle controversies, it 
seems to be of little consequence in which way it could 
be decided ; but it had, to the disputatious Greeks, 
and the more disputatious Schoolmen, a charm on 
account of its subtlety, which its value could not 
secure to it. 

(20.) Definition of Terms. 

Definition* is applied to terms in their logical use, 
and means describing them in such a manner as to 
distinguish them from all and any other terms. 
*de and fioio, more remotely finis. 



OPERATIONS WHICH RELATE TO TERMS. 59 

As much error arises from the indistinctness of 
terms, and the fact that different persons employ them 
in different meanings, just definitions which may bind 
both parties in a controversy are very important. 

A definition is usually put in the form of a catego- 
rical proposition, of which the subject is the term to 
be defined, and the predicate is the description or dis- 
tinct explanation. Thus in the example " Man is a 
rational animal" the whole sentence is called the defi- 
nition. This is not, however, strictly speaking, cor- 
rect ; as the predicate alone " rational animal" defines 
,"man," as if in answer to the question "what is the 
definition of man ? 

The first division of definition is into two kinds, 
Essential and accidental; Essential definitions are 
further divided into 'physical and logical. 

The second division of definition is into nominal 
and real. Before explaining the meaning of these 
divisions, we shall arrange them, for the sake of con- 
venient reference, into a tabular statement. 

DEFINITION". 
1st division (divided into) 2d division 



r ^ f *s 

Essential Accidental Nominal Real 

(div. into) 

Physical Logical 

An essential definition is one which presents to us 



60 LOGIC. 

the principal parts of the essence of the thing defined ; 
thus, a steamboat is " something consisting of hull, 
engine, wheel-houses, smoke-pipe, &c. ;" or, again, it 
is "a vessel for water transportation propelled by 
steam." In each case the form of our essential defi- 
nition would be induced by the character of the per- 
son asking the definition, and according to the infor- 
mation he desired, but always in terms of the essential 
parts of the object for which the term stands. But 
it must be particularly observed that these principal 
or essential parts are of two kinds widely different 
from each other : physical parts or parts which are 
actually separable by the hand, and Logical parts, or 
those which are only divisible by the mind. To ex- 
plain, a physical essential definition of a ship would 
be "an object which consists of hull, masts, cordage, 
&c," being the parts into which it may be physically 
divided ; while the logical parts which would consti- 
tute a logical essential definition would be the genus, 
viz., " ocean vessel ;" and differentia, viz., "of pecu- 
liar build;" which, as we have seen, when combined 
make up the species ship. 

(species) (genus) (differentia) 

A ship is an ocean-vessel of peculiar build. 

A logical essential definition then, in every case, 
consists of the genus and differentia. Logic is con- 
cerned with logical definitions alone, but examines 
the others to distinguish between them and logical 



OPERATIONS WHICH RELATE TO TERMS. 61 

definitions. And it is likewise true that the physical 
and logical definitions sometimes coincide, but this is 
of rare occurrence. 

An accidental definition, or description^ as it has 
been technically called, consists in presenting the cir- 
cumstances belonging to an object, and these are its 
property or accident ; as these are generally more de- 
scriptive of an animal or object than the material part 
which is the genus, or the differentia which distin- 
guishes the species in question only from its co-ordi- 
nate species. 

From what has been said before, it will appear that 
in describing a species we can only use properties, as 
accidents attach alone to individuals, while properties 
belong to every individual of a whole species : we 
should use, besides, properties which are universal and 
peculiar, since, as they belong to every individual of 
the species, and to none out of it, we thus find its own 
characteristics; whereas if we used the properties 
which were universal but not peculiar, we should only 
know characteristics which marked that species in 
common with others, and thus not define it. Thus if 
we should describe man as " a being who lived and 
breathed," this would not define or describe him justly. 
So, too, in describing an individual, as for instance 
in biographical notices, we should not use separable 
accidents which are not a permanent and necessary 
part of the object, but inseparable accidents which 
6 



62 LOGIC. 

belong necessarily and permanently to it. For exam- 
ple, if we say " William was the Duke of Xormandy 
who conquered England in 1066," we describe him by 
means of the inseparable accidents, viz.. that he was 
Duke of Xormandy, and that he conquered England. 

(21.) Nominal and Real Definitions. 

We come now to the second division of definitions, 
into nominal and real. 

A nominal definition is one which gives the mean- 
ing of the term which is used as the name of the 
thing. In brief, it defines the name. Thus, " a tele- 
scope is an instrument for viewing distant bodies.' 5 
" The photograph is a painting made by light on sen- 
sitive plates." "The decalogue is the table of the 
ten commandments." 

A real definition analyzes and explains, not the 
name of the thing, but the thing itself; enumerating, 
besides, all its important characteristics and proper- 
ties ; thus, a real definition for a telescope would be 
a treatise on the construction, powers, and uses of the 
instrument, and a real definition of the decalogue 
would be given only by reciting all its commandments. 

In the investigations of science it is evident that 
the aim is to obtain real definitions, and the fuller 
and more complete they are the greater their value ; 
but since in Logic we have only to do with the names 
of things, and not with their subject-matter, or the con- 
ceptions which they convey to us, it is evident that 



OPERATIONS WHICH RELATE TO TERMS. 63 

we only need nominal definitions and not real ; and 
indeed, with regard to matters of general information, 
a nominal definition will be sufficient to settle the 
grounds of a controversy ; for while it is the name 
that indicates the individual or the class, the definition 
explains the name. 

We may even, sometimes, provided both parties to 
an argument agree to do so, consider as a definition 
something ivhich is purely hypothetical, but which still 
partakes of the nature of a definition ; thus, for ex- 
ample, in an astronomical problem we say, « let be 
the suns place in the heavens ;" or in any case for 
purposes of illustration, <• let so and so be so and so." 
This form of definition is purely relative ; for although, 
in reality, C is not the sun's place, it is so relatively 
to the other points on the diagram. 

It must also be observed that it is not necessary to 
the justness of a definition that it should refer to real 
things, as, for example, we define an unicorn to be « a 
fabled animal, having but one horn;" and a phoenix to 
be " a bird fabled to live ivithout a mate and to rise 
from its own ashes." 

(22.) Rules for Definition. 

So important has the subject of definition been 
considered, that Logicians have laid down three rules 
for it, to which, if we adhere, we shall insure just and 
adequate definitions. 

1st. The definition must give to the mind a clearer 



64 



LOGIC. 



conception than the name of the thing defined, or it 
will be useless. 

In most of the arts and sciences this consists in 
putting a technicality into plain language, for those 
who are uninitiated ; but if I am asked to define cow, 
a word understood by every one, and say that cow is 
a ruminant quadruped, I violate the rule. In the no- 
menclature of science many technical terms give, in one 
word, what it would require much circumlocution to ex- 
press in common words. Accompanying this rule there 
is the caution that the character of the definition should 
depend upon the subject and the persons addressed. 

2d. The definition must be adequate ; that is, neither 
include other things than those necessary to define, nor 
exclude any necessary explanation of the thing defined. 

Thus, if I define bird to be " an animal that moves 
in the air by means of wings ," I am too extensive in 
my definition ; as that would include other animals 
than birds, as bats, flying fish, &c. ; and if I define 
it to be " a feathered animal that sings" that would be 
too narrow, as some birds do not sing. 

3d. The third rule is rather a caution which grows 
out of the other two than a rule like them. It is, that 
the words used in a definition should be sufficient and 
of the proper kind to define the thing. 

If we use too many words, we confuse the meaning 
and are liable to tautology ; if too few, we are liable to 
obscurity. Thus, to say that " a square is a four-sided 



OPERATIONS WHICH RELATE TO TERMS. 65 

figure with equal sides" would be true but not definite, 
as there may be drawn other parallelograms not right- 
angled, with equal sides. If we say " a parallelogram 
is a four-sided figure whose opposite sides are equal and 
parallel ;" we use too many words, as the equality of 
the sides implies the parallelism, and vice versa. 

In the first case we err, because we do not exclude, 
in our definition of the square, all other figures : in 
the second, because we allow it to be supposed that 
there are four-sided figures whose opposite sides are 
equal and not parallel. 

The examples taken are broader and more apparent 
than those in which faulty definitions are generally 
used, but they render the error more obvious, and in- 
dicate to us the character of the danger to be avoided. 

If we would see the practical necessity of defini- 
tions, we need but consider a few of the vague and 
inexact terms which we use in our ordinary speech, 
and which it seems a prevailing fashion to distort in 
their meanings. We shall recur to this subject under 
the general title of "Verbal Fallacies," but may now 
give a few illustrations of the value of exact defini- 
tions. Take for example such words as Necessity 
and Necessary, which may mean either an accordance 
with the invariable law of God, or an obedience to 
the blind decree of fate, according to the belief or 
scepticism of him who uses them. In its political sense, 
the adjective necessary has been said to be capable of 
6* E 



bb LOGIC. 

certain degrees of comparison, as in the argument urged 
in favour of the Bank of the United States,* in speak- 
ing of the means necessary for carrying out the provi- 
sions of the Constitution, it was asserted that they may 
be classed under the three categories of necessary, very 
necessary, and absolutely and indispensably necessary. 
So also in religion, certain things are said to be gene- 
rally necessary to salvation, while others are said to be 
absolutely necessary. Thus the technical sense of the 
word is entirely lost ; as that refers to an absolute 
condition, which cannot but be, or cannot be otherwise, 
and therefore does not admit of comparison. Or if we 
would see a strange, conglomerate example of indefi- 
nite and erroneous terms, demanding a clear definition, 
take the war-cry of the French revolutionists, 
"Liberty, Equality, Fraternity ;" no one word of 
which can express to the people a distinct idea, or 
will bear the test of a clear definition. 

It has been a custom in nominal definitions to de- 
fine one term by means of its synonym, borrowed 
from another language. Although our language is, in 
its structure and the great majority of its words, 
Anglo-Saxon, still the large number of French and 
Latin words which have been brought into it, have 
formed terms synonymous with the original Saxon : 
but, when they had become naturalized, as we had 
no use for two words exactly synonymous, wisdom 

* Kent's Commentaries, vol. i., Lect. 12, 



OPERATIONS WHICH RELATE TO TERMS. 67 

suggested that they should exhibit shades of difference 
in meaning, which did not originally belong to them ; 
so that few if any words are justly defined by their 
synonyms. Besides, as a similar idea among any two 
people would have its differences drawn from their own 
peculiarities of clime, and race, and manner of life and 
government, the synonyms when brought into the lan- 
guage would often express great differences at once, and 
without any effort on our part to cause them to do so. 
As a remarkable instance of this, let us see how very 
wrong it would be to define our English word freedom, 
by its synonym liberty, which comes to us from the 
Latin ; and yet, how many confound the two. Indeed 
these are historic words, and give us an insight into 
the times of their birth, wonderfully illustrative of 
the people and countries from which they came. 
Freedom is the personal, individual independence and 
right of every man, his free doom, i. e. free province or 
jurisdiction from his birth. Coming as it does from 
the Teutonic element in our language, it tells us of 
the free and independent Germans, who by their own 
valour, overturned the great fabric of the Roman 
empire. They were men of the forest and mountain, 
inhabiting no cities — there were none in Germany till 
after the eighth century — but only roving where were 
the lordliest spoils, and claiming them as the reward 
of their personal freedom. On the other hand, liberty 
tells us of the Roman cities, of the sway of the Roman 



68 LOGIC. 

empire, and of Koman licentiousness ; of a form of 
manumission, implying slavery ; individuality merged 
in citizenship ; to be a Roman citizen to have attained 
the post of honour, open to all advancement in diplo- 
macy and war. Nor is the spirit belonging to these 
words yet lost. While we cling like good citizens to 
our liberty, vouchsafed to us by the constitution of 
the country as Americans, — we much more desire to 
keep well guarded that freedom of opinion, of speech, 
of action, which is our indefeasible right as men. 

In view of the importance of just definitions, let us 
undertake no controversy, or expression of opinion in- 
volving a vague and indistinct term, without demand- 
ing a definition, and agreeing to use it during the 
discussion. 

(23.) Division. 

It is of great importance in the consideration of 
common terms which stand for classes, that we should 
be able to divide them into all their several parts or 
significates. An individual, as its name indicates,* 
is incapable of logical division. It is only a species 
or genus, i. e. a class, in more general language, 
which can be so divided. 

Division is of two kinds, physical and logical ; to 
these some writers add, improperly, numerical divi- 
sion. 

* in and dividuus, from divido, to divide. 



OPERATIONS WHICH RELATE TO TERMS. 69 

Physical division is the actual separation of the 
physical parts of which a thing is composed. It is 
evident that an individual is capable of physical divi- 
sion; thus, an individual tree, as a certain oak, may 
be divided into trunk, branches, and these further sub- 
divided into bark, heart, leaves, &c. ; an individual 
man, as John, may be physically divided into head, 
arms, trunk, legs, &c. With this kind of division 
Logic has directly nothing to do. 

Logical division, which cannot be applied to in- 
dividuals, but only to classes, consists in separating a 
genus into its different species ; and a species into the 
individuals composing it : and this in regular order 
from the summum genus to the infima species. Thus, 
the genus tree would be logically divided into oak, 
maple, hemlock, fir, pine, elm, &c. ; and the species 
oak, into red oak, white oak, live oak, scrub oak, &c. ; 
and each of these again into the individual trees com- 
prising its kind. 

It will be evident that in a just division, each one of 
the parts — denoting a species — will be less than the 
whole number which make up the genus ; or any one 
of the parts — denoting an individual — will be less than 
the whole number which make up the species ; or, as 
a test of the correctness of the division, we must be 
able to predicate the summum genus of any one of 
the parts. 

If, for example, we have assumed tree to be the 



70 LOGIC. 

summum genus, we must be able to predicate tree of 
oak, or live-oak, or any individual live-oak. 

It is evident that the same term may be logically 
divided, according to race, into Caucasians, Malays, 
&c. ; according to creeds, into Buddhists, Jews, Ma- 
homedans, Christians, &c. ; according to nation, into 
Americans, English, French, &c. These cross-divi- 
sions must not be mingled or confounded ; for ex- 
ample, to divide man into Caucasians, Mahomedans, 
Americans, &c, would be false and useless division. 

The principle of division is best illustrated by a 
scheme, or inverted tree, in which are arranged clearly, 
symmetrically, and without arbitrariness, the different 
parts of the division. 

SCHEME OP DIVISION. — SUMMUM GENUS. 

TREE. 



r 

Oak. 

a. 


"""■ " ~\ 
Maple. Pine, &c. 

A 


Live-Oak, White-Oak, Red-Oak, &c. 


r > 
Sugar-Maple, Common-Maple. 


Individual Trees. 


r ',-■'".'"> 

Individual Trees. 



It may be well to observe particularly an auxiliary 

phrase, according to, which we use to keep us from a 

simple but dangerous error. Man is divided not into 

races, creeds, nations, &c, but according to these, 

into various parts ; thus : — 

SUMMUM GENUS. — MANKIND DIVIDED ACCORDING TO. 

t A ^ 

Raco. Creed. Nation. 

„ A .. . A ,. = A. „ 



Caucasian, Malay, &c. Jews Christians, Mahomedans. English, French, German, &c. 



DIVISION. 71 

It is evident that all the co-ordinate species must 
be on the same line or platform, that is, they must 
hold the same relative position to the summum genus. 
We must be careful to omit no subaltern genus; and 
we must place each subaltern genus in its own rela- 
tive grade. Thus, if we should place oak properly, in 
the division of tree, but should pass immediately from 
the genus tree to the species sugar maple, thus leaving 
out the species maple, co-ordinate to oak, we should 
make an unequal and undue division. This would 
be placing one of the co-ordinate species on the same 
level with one subordinate to it. 

From what has been said, it will be seen that the 
process of Division is exactly the opposite of Gene- 
ralization. 

As in Generalization, we disregarded the differ- 
ences between many individuals, or between many 
species, and considered only the properties they 
had in common, that we might constitute them re- 
spectively species and genus, calling them by a common 
name; so in Division, we take the genus thus obtained 
and add to it the several differences which we had re- 
moved in Generalization, and which distinguish its 
parts, that we may call the parts thus enumerated by 
separate names. 

The two inverse processes of generalization and 
division may be plainly illustrated by a scheme or 



72 LOGIC. 

double tree ; and this may be made as full as we 
please : thus, from individual trees we may generalize 
to the genus tree ; or, from trees and shrubs and other 
kinds of vegetation, we may generalize to the sum- 
mum genus vegetable. The division will be of the 
exact species, &c, but in the inverse order. 

SCHEME OF GENERALIZATION AND DIVISION. 

Individual Trees, Individual Trees. Individual Trees. 



Live-Oak, Red-Oak, &c. 


v ' 

Sugar-Maple, Common -Maple, 


&o. 


Y 

"VFhite-Pine, Yellow-Pine, &c 

V J 


Oak. 




Y ■ 

Maple. 






Pine. 

j 






V 












TREE. 




















Oak. 




Maple. 




Whi 


Pine. 


Live-Oak, Eed-Oak, &c. 


Sugar-Maple, Birdseye-Maple, 


&c. 


te-Pine, Yellow-Pine, &c 


Individual Trees. 


r 


Individual Trees. 


/— 


Individual Trees. 



What has been called mathematical or numerical 
division is in reality but a form of physical division ; 
thus, I divide a loaf into slices, or an apple into pieces, 
physically, with or without regard to the equality of 
the pieces, or their sizes relatively to each other. If 
this equality or relation be observed, it may be called 
numerical division, but it is only an exact form of 
physical division; as a half, a third, ten times as 
great, &c, &c. 



RECAPITULATION. 73 

By a comparison of the subjects of Division and 
Definition, it will be seen that division is, after all, 
but a systematic and practical kind of definition, since 
there can be no better way to illustrate the meaning 
of tree, than logically to divide it, before our eyes, into 
all its species down to individual trees. 

It will be readily seen that the nature of the logical 
division of terms will depend much upon the science 
in which they are used, and the principle according to 
which they are to be classified. Thus an ethnologist 
would divide mankind according to races; a theologian 
according to creeds ; and a statesman according to 
nation. The principle of all the divisions would be 
the same, while the resulting cross-divisions, as we 
have seen, will be widely different. 

(24.) Recapitulation. 

It will be well to recapitulate briefly what has been 
said upon the subject of terms, and the various ope- 
rations which concern them. We have shown, 

1st. That a term is the expression of an object of 
apprehension, and have explained the different kinds 
of terms, according to a regular division. 

2d. That common terms are obtained by the pro- 
cesses of Abstraction and Generalization. 

3d. The distinction between genera, species, and 
individuals, $c. 



74 LOGIC 

4th. The Definition of terms, and just rules for 
definition. 

5th. Division of terms, with the difference between 
physical and logical division, and special considera- 
tion of the latter. 

The next step will be to combine these terms into 
propositions : that is, from our knowledge of two of 
them to assert their agreement or disagreement. 



PKOPOSITIONS. 75 



CHAPTER VI. 

(25.) Propositions. 

A proposition* is an act of judgment expressed in 
language, and consists of three parts, a subject, a 
predicate, and a copula: the subject and the predi- 
cate are called the terms or extremes of the propo- 
sition. 

The subject, in the due order, is placed first, and is 
that of which something is predicated, i. e. affirmed 
or denied. 

The 'predicate is that which is affirmed or denied of 
the subject. 

The copula is the uniting word which expresses 
the agreement or disagreement between the subject 
and predicate ; and is always some part of the verb 
to be. When the copula is affirmative, agreement is 
expressed, when negative, disagreement. 

sub. cop. pred. sub. cop. pred. 

A is B = (Caesar) is (a tyrant.) 

sub. cop. pred. sub. cop. pred. 

A (is not) B = (Csesar) (is not) (a tyrant.) 
* Frora^r opono — something proposed or set forth for our acceptance. 



7(3 LOGIC. 

The negative particle, it must be observed, is always 
a 'part of the copula. 

What appear, in our ordinary speech, to be simple 
propositions, are sometimes inverted or elliptical forms 
of expression, which must be put into simple logical 
form before they can be considered as propositions. 

Thus we say " I hope to see you," " I desire to re- 
main ;" and in these cases the subject is really placed 
last ; the true meaning being 

subj. cop. pred. 

(To see you) is (the thing which I hope, or my 
hope.} 

As an example of another form of inversion, we 
have that which springs from the constant use of the 
neuter pronoun it. Thus, in ordinary language, we 
say "It is ^true that I think so." The true logical 
form may be given thus : — 

subj. cop. pred. 

(That I think so) is (a true thing). 

Many writers have denied that there is such a thing 
as a negative- judgment ; and, consequently, that any 
negation attaches to the copula: for they say that 
the proposition John is not happy is equivalent to 
John is unhappy, which indicates a positive sensation 
or frame of mind, as well as the other ; but this is a 
quibble about words, as there are propositions in which 
the negation cannot be thus destroyed, and such is 
the case with far the greater number. The positive 



PROPOSITIONS. 77 

term is generally limited and intelligible ; the nega- 
tive unlimited and indefinite ; thus man, is a term 
which we can grasp, but not man, includes all the 
•universe beside. _J 

Of the Copula. — The copula may be always reduced 
to the present tense of the indicative mood of the 
verb to be, and consequently expresses neither past 
nor future time. Thus, " Caesar was the conqueror of 
Gaul," is equivalent to " Csesar is the historic person- 
age who conquered Gaul." "I shall be glad to see 
you ;" is the same as " I am the person who will be glad 
to see you," &c. ; but as this reduction is in general un- 
necessary, we agree to call those propositions which are 
expressed in time other than the present. Very often 
the copula and predicate are expressed together in 
one word, as " The sun shines ;" here the word shines 
may be resolved into is shining, in which is is the 
copula, and shining the predicate. And sometimes, 
in other languages, as the Latin or Greek, a proposi- 
tion is conveyed in one single word, as amo, I love or 
I am loving, *vrtto>, I am striking ; but in every case, 
a proposition may easily be placed in such a form that 
the subject, predicate, and copula are distinctly stated. 

But this definition of a proposition, as a sentence 
consisting of a subject, predicate, and copula, is evi- 
dently a physical definition, and is not sufficient for 
our purpose. The logical definition of a proposition 
is "a sentence which affirms or denies;''' here propo- 



78 LOGIC. 

sition is the species, sentence the genus, and which j 
affirms or denies is the differentia, or statement of , 
the difference between this kind of sentence and all 
others. The word proposition not having in its ety- ! 
mology this strict meaning, it is very loosely used to ; 
express almost every kind of sentence. We must be j 
careful, in Logic, to limit it to the definition just ; 
given. Hence, we should say that a categorical pro- ' 
position, in its grammatical sense, implies the indica- I 
tive mood, since absolute affirmation or denial is ex- ' 
pressed only by that mood. Thus are excluded, the ! 
imperative moocl or all commands, the subjunctive 
mood or all hypothesis, the infinitive mood, which, as 
its name indicates, is not a finite, uniting verb, but 
only a verbal noun. 

If we examine these moods a little more in detail 
we shall find, first, that even in the indicative mood, 
questions, or the interrogative form of that mood are 
excluded, for the use of a question implies that one 
of the parts of the proposition is wanting, and that 
we depend upon the answer to supply it. Thus the 
first and simplest form of the question is 
Is A B ? = Is man mortal ? 
if the answer be affirmative, then we have a right to 
the copula is, which before was wanting, and may write 
A is B == Man is mortal. 

Another form of the question is "what is A?" or 
" what is B?" the answer to which will supply us with 



PROPOSITIONS. 79 

the predicate and subject respectively. With regard 
to the subjunctive mood there are, it must be observed, 
propositions which assume that form and which are 
called hypothetical, and they come under the class of 
compound propositions, as 

If A is B, OisD. 

In almost every case the hypothesis is stated in the 
indicative rather than the subjunctive mood ; thus 

If A is B, C is D ; rather than in the form : — 

If A be B, C will be D. 

Of the infinitive mood it may be observed that there 
are various forms thus, to ride is pleasant, may be 
rendered by riding is pleasant ; horseback exercise is 
pleasant ; plainly showing that with the verbal form 
there is a substantive value. 

(26.) Propositions divided into Simple and 
Compound. 

If now, we proceed to consider first the substance 
of propositions, we shall find them divided according 
to their substance into simple and compound. 

A simple proposition is one which has but one sub- 
ject and predicate, united by the copula is or is not. 
Simple propositions are also called categorical, that is 
there is simply affirmed or denied an agreement 
between the subject and predicate. 

A compound proposition is one which has more than 
one subject or more than one predicate, and may be 
resolved into two or more simple propositions ; as 



80 logic. 

The Delaware and the Schuylkill are rivers in Penn- 
sylvania. Compound propositions are further divided 
according to their substance into categorical, condition- 
al, causal, and disjunctive. 

A compound categorical proposition, like a simple 
categorical, affirms or denies the predicate simply and 
certainly of the subject ; thus : — 

Alexander, Ocesar, and Napoleon were ambitious 
of military glory. 

A conditional proposition consists of two simple 
categoricals united by the conjunction if; thus : — 
If A is B, Qis D. 

It is usual, for convenience, to place the conjunc- 
tion first ; the first categorical — A is B — is then called 
the antecedent, and the other — C is D — the consequent. 

A causal proposition is one in which the reason of 
the truth of a simple proposition is stated, thus : 
Because A is B, is D. 

A Disjunctive proposition is one in which one of 
two simple propositions is asserted to be true ; thus, 
Either A is B, or is D. 

This is done by the use of the conjunctions either 
and or. 

Propositions are still further divided according to 
two of Aristotle's categories which will be considered 
hereafter, i. e., according to their quantity and qua- 
lity. In simple language Quantity considers of how 
much of the subject the predicate is affirmed or 
denied ; as, some or all A is B. 



PROPOSITIONS. 81 

And Quality regards the kind or manner of that 
predication, i. e. whether it be affirmative or negative : 
whether A is or is not B. / 

(27.) Quantity and Quality of Propositions. 

The quantity of a proposition is determined bj the 
comprehension of its subject. If we assert that the 
predicate agrees or disagrees with the whole subject, 
that is, all the significates which come under the 
term, the proposition is said to be universal, thus, 

All men are mortal, No men are trees : 
are universal propositions, because the whole of the 
subject is considered. But if we assert the predicate 
to agree or to disagree with only a part of the sub- 
ject, the proposition is called 'particular. 

Some men are brave; feiv men are good ; many 
men are not prudent ; are examples of particular pro- 
positions. 

The quality of propositions we shall find also to be 
of two kinds ; the quality of the subject-matter, and 
the quality of the expression. Propositions are divi- 
ded according to the quality of the subject-matter into 
true and false % and, according to the form of expres- 
sion, into affirmative and negative. 

It is evident that with the quality of the subject- 
matter, Logic has directly nothing to do ; for since the 
logical form of a proposition is A is B, it is taken 
for granted, as we have already seen, that this state- 



82 LOGIC. 

ment is true, and that, from the very form it assumes. 
With the subtleties of statements Logic is not con- 
cerned : taking for granted the truth of a proposition, 
it makes use of it properly ; whatever falsity lies in 
it will pervade the argument, but this will not be the 
fault of Logic. In Logic the Quality of the subject- 
matter is accidental and not essential. 

The essential quality of propositions in Logic is 
then the quality of the expression : and this quality 
is made, as before shown, to depend upon the copula. 
If the copula is affirmative, the proposition is called 
affirmative; as 

All A is B. 
Some A is B. 

If the copula is negative, the proposition is said to be 
negative; as 

No A is B. 
Some A is not B. 

To mark these divisions according to quantity and 
quality, and to simplify the future operations in which 
they are used to frame arguments, we employ letters 
as symbols. Since every proposition must be univer- 
sal or particular, and at the same time affirmative or 
negative, there are four and only four classes of sim- 
ple categorical propositions, which we represent by 
the following symbols : — 

Universal affirmative : as All X is Y, by A. 

Universal negative ; as No X is Y, by E. 

Particular affirmative ; as Some X is Y, by /. 

Particular negative ; as Some X is not Y, by 0. 



PROPOSITIONS. 83 

The sign of a universal proposition is the same as 
that of a distributed term; i. e., the prefix All or 
Every for the universal affirmative, and No for a uni- 
versal negative : 

And here it must be particularly observed that the 
universal negative is only correctly written when in 
the form No A is B. It might at first sight seem 
that this is equivalent to All A is not B ; but it is 
not so, although often meant to be so: Thus all 
soldiers are not cruel, has a very different meaning 
from no soldiers are cruel. The first is not indeed a 
universal proposition as it appears to be, but a parti- 
cular, implying that some soldiers are cruel, while 
some are not. 

The translators of our English Bible have, in a few 
instances, made use of this form improperly to express 
a universal. Thus, the Hebrew text of the Psalms 
expresses with regard to the wicked: — "All his 
thoughts are < there is no God ;' " while the translators 
have it " God is not in all his thoughts ;" the mean- 
ing of the translators in this is evidently » God is not 
in any of his thoughts." 

The sign of a particular proposition is the same as 
that of an undistributed term, — i. e. the prefix some, 
few, several, many, and like words, indicating a part 
only of a whole, for particular affirmative propositions ; 
and the same prefix, with a negative copula, for par- 
ticular negative. 



84 LOGIC. 

But it constantly happens that a proposition has no 
prefix, and we are then thrown upon our knowledge 
of the subject-matter of the proposition to determine 
whether it be universal or particular. Such propo- 
sitions as have no prefix to denote their quantity are 
called indefinite propositions, which Logic alone will 
not enable us to understand. We must then look to 
their meaning, and thus find out what prefix is their 
due. For example, — Men are artists. 

By examining the matter of this, we find that only 
some men are artists, and then making the proper 
prefix we declare the proposition to be particular. 

Birds fly. This is true of birds universally, and 
we have the right to prefix the sign all, which de- 
notes it a universal proposition. 

A Singular proposition is one which has for its sub- 
ject a singular term ; as 

Alexander was a conqueror. 
Caesar was ambitious. 

It would seem at a first consideration of the quan- 
tity of these propositions, that they were particular, 
but this is erroneous ; they are evidently universal ; 
since when I assert that Alexander was a conqueror, 
I mean the whole of Alexander, or Alexander taken 
in his.fullest extension. 

As a general rule, then, singular propositions are 
universal. There are many other divisions of pro- 
positions which are curious rather than useful dis- 



PROPOSITIONS. 85 

tinctions. The above are all those necessary to a 
comprehension of the logical processes which follow. 

(28.) Of the Distribution of Terms in Propo- 
sitions. 

Having treated of the quantity and quality of pro- 
positions, and observing that, as we have already seen, 
these propositions are to be hereafter used in the 
framing of syllogisms, we come to consider the dis- 
tribution of terms in propositions, and to establish 
rules for this distribution. If we examine the four 
categorical propositions, with their geometrical nota- 
tions, — 

Aff . 4. J All X is Y. Won . ^./NoXisY. 

Atnrm. /. | Some X is Y. - Neg * 0. \ Some X is not Y. 

(A) (I) (E) 




:©©0 




first with reference to their subjects, it will be evident 
that in A and E the whole of the subject being con- 
sidered, the subject is distributed., as is also indicated 
by the prefixes All and No. It will be equally evident 
that in I and the subject is undistributed, a portion 
only being taken, as is indicated by the prefix Some. 

The rule deduced then, as far as the subjects are 
concerned, is very simple ; it is, that 

All universal propositions distribute the subject. 
No 'particulars distribute the subject. 



86 LOGIC. 

But since the predicates in these propositions have 
no such prefixes, how are we to determine whether 
they are distributed or undistributed ? By an exami- 
nation of the relation existing between the subject 
and predicate in each case, we shall see that the dis- 
tribution of the subject by no means implies that of 
the predicate. 

If we assert, 1st that All X is Y, we do not assert 
that other things likewise may not be contained in 
Y ; for though All X is Y, All W may be Z, All Z 
may be Y, &c. ; or, to illustrate by a geometrical 
figure, we have 




and still space enough for other things to be contained 
in Y. Hence, it is evident that the whole of Y is 
not considered in the proposition all X is F, or that 
Y, the predicate, is not distributed in a universal 
aflirmative proposition. 

Again, if we take the proposition some X is Y, the 
same reasoning will apply, since many other things 
may be Y, besides this some X; as is illustrated in 
the figure 



PROPOSITIONS. 8T 

Likewise then we see that the whole of Y is not 
taken in this case, or that the predicate of a particu- 
lar affirmative proposition is not distributed. 

Thus far, then, we have found it true of affirmative 
propositions, whether they be universal or particular, 
that they do not distribute the predicate. 

If now, we consider the universal negative, no X 
is Y, we shall find that we must consider the whole 
of X and the whole of Y, before we can assert that 
no part of one belongs to any part of the other : — 
thus 



t:w 



We have already seen that the subject X is distribu- 
ted, and it thus appears that in a universal negative 
proposition the predicate also is distributed. The 
whole of the subject is brought in contact with the 
whole of the predicate, or we could not entirely deny 
their agreement. It remains now to consider only 
the predicate of a particular negative, some X is not 
Y. The same reasoning applies here as in the last 
case ; or we must know and consider the whole of Y, 
before we can assert that no part of it belongs to the 
some X in question. 




88 LOGIC. 

It therefore appears that the predicate of a particular 
negative proposition is distributed. 

If we collect together these four results, we shall 
thus establish two rules : 

1st. The subjects of universal propositions, and 
not of particulars, are distributed. 

2d. The predicates of negative propositions, and 
not of affirmatives, are distributed. 

It may be well, for the sake of convenient refer- 
ence, to arrange the quantity and quality of proposi- 
tions, and the distribution of the terms, in a tabular 
form, so that it may be referred to until it be fixed in 
the mind of the student. 



Frur dasaa of QriegariaH 
Propositions. 


Subject. 


Predicate. 


Simple Form. 


A. Universal afiirmatiTe. 


Distributed. 


Undistributed. 


All X is T. 


E. UniT%r 


Distributed. 


Distributed. 


So X is V. 


L Particular affinr.i: 


Undistributed. 


Undistributed. 


Some X . 


0. Particular negative. 


Undistr. 


Distributed. 


Some X : 



There is a logical process which is passed upon pro- 
positions and upon propositions only, and this process 
has in view the use which we make of propositions in 
the framing of arguments. It is called Conversion. 
We cannot convert a term, nor is it proper to speak 
technically, as some writers have done, of the conver- 
sion of arguments. 

(29.) Conversion. 

Conversion consists in transposing the terms of a 
proposition in such a manner as to place the subject 



conVeusion. 89 

for the predicate, and the predicate for the subject. 
Thus, having the proposition A is B, we convert it 
into B is A. When no other change than this is 
made, the conversion is called simple conversion : but 
by an examination of tlie four forms of categorical 
propositions, it will be evident that they cannot all be 
simply converted, and retain in the converted propo- 
sition or converse the truth of the original proposition 
or exposita. As a simple example of this ; having 
the proposition 

All men are mortal ; 

we cannot write the converse, 

All mortals are men. 

No other conversion is allowed in Logic than that 
which is called illative,* or that in which we may infer 
the truth of the converse from the truth of the ex- 
posita. 

To simplify this, let us convert each of these propo- 
sitions in turn. 

1st. (A.) All X is T '-== All men are mortals. 

It is evident, as we have already seen, that we 
cannot convert this proposition simply, for we can- 
not read 

All Y is X = All mortals are men, 

since Y(oy mortals) includes many other races besides 
men. 

We, therefore, limit the quantity of the proposi- 

* in and/e?-o, {latum). 
8* 



90 LOGIC. 

tion from universal to particular, so that Y, which was 
undistributed in the original ^proposition, may remain 
so in the converse. Expressing then this non-distribu- 
tion of Y fey the prefix some, we shall have as the 
converse 

Some Y is X ' = Some mortals are men. 

From the nature of the process, this form of illative 
conversion is called conversion by limitation.* 

From this we see that the converse of a universal 
affirmative is a particular affirmative, or A becomes, 
when converted, I. If we examine the universal 
negative, 

2. (E.) No X is Y = No men are trees, 

we shall see that as X and I^are taken in their whole 
extension, or are distributed, we may here convert 
simply, and read 

No Y is X = No trees are men. 

(JvolODhe converse of a universal negative is a universal 
negative. 

So, likewise, in the particular affirmative 
3. (I.) Some X\s Y = Some men are cruel, 

we shall find that neither subject nor predicate is taken 
in its full extent or distributed, and that we may, 
therefore, convert simply : 

Some Y is X = Some cruel (beings) are men. 

*The Latin name employed by logicians, for this kind of con- 
version, is conversio per accidens. 



CONVERSION. 91 

The converse of a particular affirmative remains a Kijb^. 
particular affirmative. There remains only the parti- 
cular negative to be considered. 

4. (0.) Some X is not Y = Some quadrupeds are not horses. 

This proposition presents a special difficulty. We 
cannot convert it simply as in the cases of E and I ; 
for we should then have X, which is undistributed in 
the exposita, distributed in the converse; thus we 
would have the absurdity 

Some Y is not X = Some horses are not quadrupeds. 

Nor can we invert the process of conversion by limi- 
tation as in the case of A (1.,) and pass back from 
particular to universal, as 

All Y is not X = All horses are not quadrupeds. 

To overcome this difficulty we detach the negative 
particle not in the original proposition from the copula, 
and attach it to the predicate ; thus, instead of the 
open form some X. is not Y, we read, 

Some X is (not Y) = Some quadrupeds are (not horses). 

and then it is evident that for all logical purposes, 
the proposition ceases to be or particular negative, 
and becomes I or particular affirmative, since for (not 
Y) we might place any other symbol, as Z, and convert 
by simple conversion. But without this trouble, if we 
convert we shall have 

Some (not Y) is X = Some {not horses) are quadrupeds, 

or in our ordinary language, to complete the sense : 

Some (beings which are) not horses are quadrupeds. 



92 LOGIC. 

v\\$ r ( This is called conversion by contraposition or by nega- 
tion. 

We arrive by this process at a rule for illative con- 
version — which is, that No term must be distributed in 
the converse which was undistributed in the exposita. 

By arranging the different kinds of illative conver- 
sion in tabular form, we shall simplify them for refer- 
ence. Taking the letter p to indicate conversion by 
limitation or per accidens ; s, simple conversion ; and 
k, conversion by negation, we shall have the following 
table. 

ILLATIVE CONVERSION. 

Original Propositions. Methods of Converting. Converted Propositions. 

(A.) All X is Y. p. Some Y is X. (I.) 

(E.) No X is Y. s. No Y is X. (E.) 

(I.) Some X is Y. s. Some Y is X. (I.) 

(0.) Some X is not Y. Tc. Some (not Y) is X. (I.) 

The above are the regular forms of conversion, but 
there are certain Additional conversions to be noticed. 
It must be remarked that the universal affirmative, 

All X is T ' = All men are mortals, 

is sometimes converted in another manner, i. e. by 
putting immediately before both subject and predicate 
the negative particle not, and then converting, thus 

All (not) Y is (not) X = All (not) mortals are (not) men. 

i. e., All (who are not) mortals are not men ; or in 
common phrase, None but Y can be X == none but 
mortals can be men. 

Again, (E), which is converted simply, may be like- 



CONVERSION. 93 

wise converted by limitation, since, if having the uni- 
versal form 

No A is B = No men are trees, 

we can say 

No B is A = No trees are men, 

we can also say, what is less 'than this, 

Some B is not A = Some trees are not men. 

It may happen that for some purpose of logical 
technicality it will be better to use the particular when 
we have a right to use the universal, but from the ex- 
istence of the universal we infer that of the particu- 
lar, which is only a part of it. 

There remains only one remark to be made upon 
the subject of conversion ; it is that there are a few 
propositions which bear the form of A or universal 
affirmative, which are capable of simple conversion. 
The terms of such a proposition are said to be con- 
vertible terms, or the predicate and subject are either 
exactly equivalent or exactly co-extensive : for exam- 
ple in the proposition All common salt is chloride of 
sodium, we have a right to assert that all chloride of 
sodium is common salt. From the proposition All the 
good are saved, we have a right to infer that All (who 
are) saved are good. Many just definitions come 
under this class. Besides such propositions as these, 
there are many mathematical propositions which seem 
to be single propositions with convertible terms, when 
in reality they contain two distinct propositions, each 



94 LOGIC. 

of which requires distinct proof. Thus, All equila- 
teral triangles are equi-angular. The apparent con- 
verse that All equi-angular triangles are equilateral, 
is indeed true, but this is not inferred from the origi- 
nal proposition, it is proved separately by geometri- 
cians ; so that instead of being the converse of the 
proposition stated, it is, in reality, a distinct propo- 
sition. 

The processes of conversion have been applied 
above only to the forms of simple categorical propo- 
sitions; they may likewise be applied, however, to 
compound propositions, and when we come to con- 
sider these, we shall show how they may be converted ; 
but it may be here observed, that as all compound 
propositions may be readily reduced to the simple 
categorical form, having shown how to convert these, 
we have in reality shown how to convert them all. 

The next process of importance in considering pro- 
positions, is the manner and character of their oppo- 
sition to. each other, and this, like the process of 
conversion, becomes of special value when we are 
joining propositions together to frame arguments. 

(30-) Of Opposition. 
Two propositions are said to be opposed to each 
other, when, having the same subject and predicate, 
the one denies either entirely or in part what the other 



OPPOSITION. 95 

affirms, or affirms either entirely or in part what the 
other denies; as, for instance, the proposition 

(A.) All men are mortal, is opposed by both {^TZeTaZZof mortal, gg 
and (E.) No angels are men, is opposed by both { f^^alarlZen. £} 

Again, two propositions are said to be opposed 
when, having the same subject and predicate, the one 
affirms in whole what the other affirms in fart, or de- 
nies in whole what the other denies in part, Thus : 

(A.) All men are mortal, (Opp.) Some men are mortal. (I.) 
(E.) No men are trees, {Opp.) Some men are not trees. (0.) 

It will appear, then, that the opposition in propo- 
sitions is both in quantity and in quality, and as there 
are four forms of categorical propositions, and any 
two may be thus opposed, we shall have four kinds 
of opposition, which will best be illustrated by the 
following figure:- _ 

A contraries E ffl j *<* *■* (j 

s V -» - t 



X & 






I ■ sub-contraries O 

In which the two universal propositions A and E are 
called contraries and differ only in quality, being re- 
spectively affirmative and negative; the two particu- 
lars I and are called sub-contraries, differing 
likewise in quality only ; the two affirmatives and the 
two negatives are called respectively subalterns, differ 



<p 



96 LOGIC. 

ing in quantity only ; the universal affirmative and 
particular negative, and the universal negative and 
•particular affirmative, are respectively called contra- 
dictories, and differ both in quantity and quality. 

If we desire, as in applying Logic we may do, to 
determine the relative truth and falsity of these re- 
spective propositions, we must look for a moment at 
the matter which they may contain. 

(31.) Of the Matter of Propositions. 

The matter of a proposition is the nature of the 
union betiveen the terms of the proposition, or in ordi- 
nary language, the exact meaning of the proposition. 

By considering the nature of this connexion be- 
tween the terms, we shall see that it can be of only 
three kinds : necessary, which is expressed by an 
affirmative proposition ; impossible, expressed by a 
negative proposition, and contingent, which is ex- 
pressed by a particular proposition. 

To illustrate : if we have given to us the two terms, 
men and mortal, and are told to connect them by a 
copula, we ask ourselves, what is the nature of the 
connexion between these two. The answer is, it is 
necessary, and we express that necessity by using an 
. affirmative copula, and prefixing the sign All : 
All men are mortal. 

Again if we have given to us the two terms men and 



opposition. 97 

trees, to perform an analogous operation, we shall 
assert the nature of the connexion between them to 
be impossible, and express that impossibility by the 
use of the prefix JVo — 

No men are trees. 

If again, we have the terms men and handsome, we 
assert the nature of the connexion to be contingent, 
as some men are and some are not handsome, and thus 
to express contingent matter we write the proposition 
with the prefix some ; 

Some men are handsome. 
Some men are not handsome. 

If, now, we examine the matter of these propositions 
we shall see that 

In necessary matter all affirmatives are true, and 
negatives false. 

Necessary Matter. 

True. False. 

(A) All men are mortal. (E) No men are mortal. 

(I) Some men are mortal. (0) Some men are not mortal. 

In impossible matter all negatives are true and affirma- 
tives false. 

Impossible Matter. 

True. False. 

(E) No men are trees. (A) All men are trees. 

(0) Some men are not trees. (I) Some men are trees. 

In contingent matter all particulars are true and 
universals false. 

9 G 



y» LOGIC. 

Contingent Matter. 

True. False. 

(I) Some men are handsome. (A) All men are handsome. 

(0) Some men are not handsome. (E) No men are handsome. 

From this examination we perceive that if one con- 
trary is true the other must be false, but if one is 
false the other may be false also : if one sub-contrary 
is false the other must be true, but if one is true the 
other may be true also. But in the case of contra- 
dictories, if one is either true or false, the other must 
be just the opposite, i. e., false or true. 

It remains to consider the subalterns, which differ 
in quantity. If the universal (A or E) be true, the 
particular I or will be true also ; as 

(A) All men are mortal, (E) No men are trees, 

implies implies 

(I) Some men are mortal. (0) Some men are not trees. 

If the particular I or be true, the universal A 
or E is not necessarily true. 

(I) Some islands are fertile, does not permit us to 
infer (A), All islands are fertile. 

(0) Some islands are not fertile, does not permit us 
to imply (E) No islands are fertile. 

But if the particular be false, the universal must 
of necessity be false also. Thus the false particular 
Some men are trees, would give us also All men are 
trees as a false universal. 

By summing up these inferences we may state the 



COMPOUND PROPOSITIONS. 99 

following rules, which must be kept in the memory as 
we approach the subject of Reduction. 

I. Contraries may both be false, but never both be 
true. 

II. Sub-contraries may both be true, but never 
both false. 

III. Of Contradictories, if one be false the other 
must be true, and vice versa. 

IV. In Subalterns we reason from the affirmation 
only of the universal to the affirmation of the parti- 
cular ; but from the denial of the particular to the 
denial of the universal. 

With the remark that opposition may be also illus- 
trated in compound propositions or those not directly 
in the simple categorical form ; or that such proposi- 
tions may be reduced to this simple form, by an easy 
process still to be explained ; we pass to the subject 
of compound propositions. 

(32.) Of Compound Propositions. 

A compound proposition consists of two or more 
simple propositions, united together either by a simple 
copulate, expressed or understood, or by a conjunc- 
tion denoting an hypothesis. 

Compound propositions are consequently divided 
into two classes, categorical and hypothetical. 

Compound categorical propositions are of two kinds, 
copulative and discretive. 

Ltffc 



100 LOGIC. 

A copulative proposition consists of two or more 
subjects united with the same predicate, or with two 
or more predicates, by the use of the copulative con- 
junction, as 

Men, horses, and birds are animals. 

A discretive proposition consists of two simple pro- 
positions, which are contrasted on account of an appa- 
rent inconsistency, as 

Fox, though dissolute, was a patriot. 
Many compound propositions are tacit or implied, 
and thus have the form of simple propositions. 

A hypothetical proposition consists of two or more 
simple propositions united by a conjunction which 
expresses hypothesis. This conjunction is usually 
placed at the beginning of the proposition. 

Hypothetic als are divided into conditional, disjunc- 
tive and causal, and take these names from the con- 
junctions which express the condition of the hypo- 
thesis. 

A conditional proposition expresses the condition 
by the conjunction if; as 

If A is B, C is D = If John return, Harry will go. 
- t A disjunctive proposition is formed with the con- 
junctions either and or; as 

Either A is B, or C is D = Either the day will he fine or cloudy. 
A causal proposition unites its parts by the con- 
junction because ; as 

A is B, because C is D. 
John is well because he is prudent. 



COMPOUND PROPOSITION. 101 

It is evident in the case of categorical propositions, 
that they may be at once resolved into the simple 
propositions of which they are composed : thus we 
may divide the copulative proposition given into three 
distinct propositions ; viz., 

Men are animals, 
Horses are animals, 
Birds are animals, 

and the discretive may be divided into two ; thus : — 

Fox was dissolute. 
Fox was a patriot. 

Unlike the compound categorical propositions, the 
hypothetical* contain within themselves the germ of an 
argument, and only require that the hypothesis shall 
he established or fail of establishment, to arrive at a 
conclusion. Thus, having the proposition, 

If A is B, C is D, 
we need only know whether A is B, in order to 
state the argument and arrive at the conclusion that 
C is D. 

Conditional propositions, however, may be, in every 
case, reduced to a categorical form, by regarding them 
as universal affirmative categorical propositions, of 
which the antecedent is the subject, and the consequent 
the predicate. We then rid ourselves of the condition, 
by the use of the words, "the case of;" thus, instead 
of the form, If A is B, C is D, we shall have 

{The case of) A being B, is (the case of) C being D, 

which is purely categorical in form. 
9* 



102 LOGIC. 

Disjunctive propositions may be reduced to con- 
ditionals ; thus : 

Either A is B, or C is D, is equivalent to If A is not B, C is D, 
or we may place it at once in a categorical form with- 
out this double process, by reading it thus : 

The two possible cases in this matter are that A is B, and that C is D. 

It is more usual to reduce the disjunctive however 
to a conditional form, into which it very naturally 
falls. 

The causal proposition, 

Because A is B, C is D, 
becomes either at once categorical, when we establish 
the truth of because, and thus we have 

A is B, therefore C is D, 
as an enthymeme, to which, having the subject-matter, 
we might supply the wanting premiss ; or the causal 
proposition becomes simply conditional, if the cause — 
expressed by the first proposition A is B — be doubt- 
ful, and then we read, 

If A is B, C is D, 

which must be treated like the conditional above. 

As it seems, then, that all these are reducible to 
the conditional form, we need only show how the pro- 
cess of conversion is applied to conditionals, in order 
virtually to apply it to them all. From what has 
been said, it will appear that conditionals are con- 



THE NEW ANALYTIC. 103 

verted by negation only ; thus, to convert the propo- 
sition, 

If John has the smallpox he is sick ; 
we may read — 

If John is not sick he has not the smallpox, 

or, the conversion rests upon the fact that the denial 
of the consequent leads to the denial of the antecedent. 
We cannot convert without this negation, for we 
could not reason from the affirmation of the conse- 
quent to the affirmation of the antecedent ; thus, 

If John is sick he has the smallpox, 
since that consequent (sickness), may have sprung from 
some other antecedent than the smallpox. 

(33.) The Neiv Analytic. 

And here it becomes necessary, before closing the 
subject of propositions, to refer briefly to the effort 
of certain late writers to quantify the predicate ; that 
is, to place prefixes before it similar to those placed 
before the subjects of propositions to determine at a 
glance its distribution or non-distribution, and to form 
thus a new set or class of categorical propositions. 
Thus, instead of the form all men are animals, they 
would write all men are some animals, and claim 
thereby not only a greater precision in the logical 
statement, but in some instances the establishment 
of a distinct proposition ; as, for example, 
All A is (all) B. 

It may be admitted that sometimes a new idea is 
suggested by such a quantification of the predicate, 



104 LOGIC. 

but it is only suggested, not contained in the proposi- 
tion thus rendered. Thus if we say 

All men are sinners, 

we mean, by our rule, some sinners ; now the question 
as to the comprehension of this word sinners may 
arise, when we place such a prefix ; whether angels 
and devils may or may not be included in it ; and 
whether the ill-conduct of brutes is excluded from it. 
Whereas, if we could write, 

All men are (all) sinners, 

we should exclude at once all other beings from the 
category. Hence, the quantification of the predicate, 
which in the old system is implied, does when expressed, 
suggest new thoughts or judgments, but those new judg- 
ments rest upon their own basis, and have really 
nothing to do with the original proposition. There 
seems really, therefore, nothing gained in the exten- 
sion of the proposition by this attempt to quantify the 
predicate, but rather a confusion of judgment and a 
complication of logical forms. 

It is not intended to give, in detail, the applications 
of the "new analytic," nor to deny that results, 
totally out of the province of Logic, are attained by 
it. It is evident that if we quantify the predicate, in 
categorical propositions, we shall have four additional 
forms, viz. : 

Established Forms. New Forms. 

A. All A is B. All A is all B. X. 

E. No A is B. No A is some B. Y. 

I. Some A is B Some A is all B. U. 

Some A is not B. Some A is not some B. Z. 



THE NEW ANALYTIC. 105 

Now of these new forms we have already considered 
X, as in the case 

All equilateral triangles are [all) equi-angular, 

and in the cases of exact definitions, as 

All common salt is [all) chloride of sodium, 

In the first we have seen that there are two distinct 
propositions , and in the second that there are but two 
names for the same object. 

As for Y, U, and Z, they are so clearly contained 
in the old forms that they need but little elucidation. 

U. Some trees are all oaks, 

when converted gives us 

All oaks are trees. or A. 

Y. No heroes are some men, 

Conv. Some men are not heroes. 0. 

Z. Some quadrupeds are not some horses, 

by which we determine that the quadrupeds referred 
to may belong to other species, or may be included in 
the species horse, apart from the some horses men- 
tioned. 




It was attempted, in the new analytic, to simplify the 
subject of conversion, but, it seems, with inadequate 
results. 

And here we leave the subject of quantifying the 
predicate so far as it relates to propositions alone. 
If carried out in the syllogism, it would much enlarge 
the domain of Figure, and give much fruitless labour 
to the logician. 



106 LOGIC. 



CHAPTER VII. 

(34.) Of Arguments. 

An argument is an act of reasoning or ratiocina- 
tion. It consists of two parts ; that to be proven, 
and that by which it is proven. 

The part to be proven is embodied in the conclusion, 
and that by which it is proven is embodied in the 
premisses. When these are inverted from the usual 
logical order, so that the conclusion is stated first, it 
is called the question ; and the premisses which are 
joined to it by the word because, are then called the 
reason; thus, 

(Question) Why are all Americans mortal? 
or All Americans are mortal, 
Because They are men. 

But in logical form and order the premisses are stated 
first, and the conclusion is connected with them by 
the illative conjunction therefore ; thus 

Premisses J All men are mortal, 

I All Americans are men, 
Therefore All Americans are mortal. 



ARGUMENTS. 107 

These two forms must be distinguished from what is 
expressed by the words inference and proof, which 
have not to do with the order of the parts in an argu- 
ment, but with the special design of the person who 
uses the argument, i. e., whether from known facts or 
premisses, he seeks to establish a conclusion; or has 
adopted a conclusion, and is simply seeking for pre- 
misses by which to substantiate it. 

Logic teaches us to draw from known proofs only 
a just inference, or to maintain a given inference only 
by just proofs. We may more clearly illustrate by 
observing how, in the various professions, these 
different methods are used; thus, a naturalist gets 
together many observations and makes many experi- 
ments, forming a strong store of proofs, before he 
may justly infer a conclusion; while an advocate at 
law, assumes the innocence of his client or the guilt 
of the prisoner, as a foregone conclusion, and then 
uses every means for obtaining proofs and thus estab- 
lishing premisses by which to substantiate his con- 
clusion. 

It has been observed that the logical form of an 
argument is a syllogism, which consists of three pro- 
positions, i. e. two premisses and a conclusion. 

After fully explaining the syllogism, we shall con- 
sider all forms of irregular and abridged arguments, 
and show, as has been asserted, that they may all be 



108 LOGIC. 

reduced to this simple form, so that the logical tests 
may be at once applied to them. / 

(35.) Of the Syllogism. 

In the analysis of Logic, the dictum of Aristotle 
was distinctly laid down and illustrated. Its form 
was : — 

No. 1. No. 2. 

All A is B. No A is B. 

All or some C is A. All or some C is A. 

All or some C is B. No C is B, or some C is not B. 

The principle of the dictum is, that whatever (B) 
we predicate (in the major premiss) of the whole class 
(All A) ; under which class we assert (in the minor 
premiss) certain individuals (All or some C) to be 
ranged ; we may also predicate (in the conclusion) of 
those individuals. 

Thus, B is predicated of (All A), C is an individual 
of the class A, therefore we have a right to predicate 
B of C. 

But, as few arguments, in the ordinary uses of lan- 
guage, are placed in this exact form (although all 
valid arguments may be), there have been laid down 
two logical axioms and several important rules for 
determining the validity of syllogisms, without the 
labour of bringing them to this form. 

It must be constantly remembered that it is a con- 
dition of every syllogism that it contains three and 
only three terms : the major term, the minor term, and 



THE SYLLOGISM. 109 

the middle term. The first two of these terms must 
not be confounded with the 'premisses which bear the 
same name, and which are propositions. Thus in the 
example, 

mid. maj. mid. maj. 

Maj. prem. A is B = All men are mortal. 

min. ( mid. minor. mid. 

Min. prem. C is A = All Americans are men. 

min. _ maj. minor. major. 

Concl. C is B = All Americans are mortal, 

B is the major term, and it is in the major premiss ; 
C is the minor term, and it is found in the minor pre- 
miss ; A is the middle term, because it is the medium 
of comparison between the other two. In the major 
premiss, the middle term is compared with the major ; 
in the minor premiss it is compared with the minor, 
and in the conclusion, the minor and major terms, 
having been thus found to agree with the same middle 
term, are asserted to agree with each other. 

The minor term is always the subject of the con-, 
elusion, and the major term the predicate. 

This simple process of comparison leads us to thtK 
statement of those axioms which determine the con- 
ditions of agreement and disagreement between the 
major and minor terms, and to note some important 
consequences following from them. 

(36.) Logical Axioms. 

1st, If two terms agree with one and the same third 

term, they will agree with each other. 
10 



110 LOGIC. 

2d. If of two terms, the one agree and the other 
disagree with one and the same third term, they will 
disagree with each other. 

Rules. 

I. From the first of these axioms we observe that 
if both premisses of a syllogism are affirmative, thus 
expressing the agreement of the major and minor 
terms with the middle, the conclusion must likewise 
be affirmative, or express the agreement between these 
two terms ; thus, B being the major term, C the minor, 
and A the middle, we have 

A is (or agrees with) B, 
C is (or agrees with) A, 

and we must consequently state the 

conclusion 

C is (or agrees with) B. 

II. Again, from the second axiom, we see that if 
one of the premisses (as the major) be affirmative, and 
thus express the agreement between the major term 
and the middle, and the other be negative and thus 
express a disagreement between the minor term and 
the middle, we must have a negative conclusion to 
express the disagreement between the major and the 
minor, which we have thus shown, the one to agree 
and the other to disagree in the premisses with one 
and the same third {the middle). 

Thus if, A is not (or disagrees ivith) B, 



THE SYLLOGISM. Ill 

And if, C is (or agrees with) A, 
we must have, C is not (or disagrees with) B. 

III. It is further evident that if both premisses be 
negative, we can draw no conclusion ; because in these 
premisses the middle term, simply disagreeing with 
both the major and minor terms, is no longer a 
medium of comparison between them. For example, 
state the premisses, 

No A is B = No men are trees, 
No C is A = No horses are men ; — 

we have established no relation whatever between C 
and B, or between "horses and trees, so that, although 
we might truthfully write 

No horses are trees, 

it would be an accidental statement, and not spring 
from the premisses stated. 
/^ In the conclusion is stated the relation between the 
major and minor term, which was established in the 
premisses by the medium of the middle term. The 
•minor term is the true subject of the conclusion, and 
the major term the true predicate. Sometimes in an 
inverted or elliptical conclusion these terms may 
appear transposed, but when properly written out 
they will take the places indicated. 

The middle term, which occurs twice in the pre- 
misses, is the medium of comparison between the two 



V 



112 LOGIC. 

other terms, and is generally the name of a class, of 
which in one premiss something is predicated, or to 
which some quality is attributed, as 

1. Man is a rational animal, 

in which man is the name of a class, and rationality 
a predicate or attribute : under which in the other 
premiss we range an individual or individuals belong- 
ing to the class, as 

2. John is a man, 

and by means of which we have a right to predicate 
or attribute this same thing rationality to the indivi- 
dual; thus, 

3. John is a rational animal. 

IV. Ambiguous middle. 

It is scarcely necessary to state that the middle 
term must be univocal, i. e., must have the same 
meaning in both premisses. If it be ambiguous, or 
possess one meaning in the major premiss and a differ- 
ent one in the minor, we shall violate the first princi- 
ple in the construction of a syllogism, and have four 
terms instead of the three, and only three, required. 
Most languages have many such ambiguous words, 
and the English particularly is full of them : thus 

1. A bank is a financial institution, 

2. The margin of a stream is a bank, 

3. The margin of a stream is a financial institution. 



THE SYLLOGISM. 113 

Many such glaring examples will occur at once to the 
student ; but it must be remembered that the sophist 
who would construct his artful fallacies to deceive, 
does not employ such manifestly ambiguous words, 
but those whose double meanings are much more 
nearly the same. 

Thus, in their philosophic meanings, the words 
church and faith have given rise to sharp controversy 
and violent partisanships. As ambiguous terms play 
a very prominent part in the subject of Fallacies, we 
shall recur to them under that head. 

When the argument is written out in symbols, the 
ambiguity either disappears entirely, that is, when we 
represent the term in both premisses by the same 
letter, thus 

Cis J, 
C isB, 

or it becomes at once manifest, when we represent the 
term in the major premiss, by one symbol, as A, and 
that in the minor, having a different meaning, by ano- 
ther, as D, thus 

AisB, 

CisD, 

in which premisses there are four terms, and the error 
distinctly appears. 

Y. Undistributed middle. 

The middle term must be distributed, i. £., taken in 
10* H 



114 LOGIC. 

its whole comprehension, at least in one of the pre- 
misses, for it will otherwise occur that we may com- 
pare the major term with one part of the middle, and 
the minor with another pari, and thus it would fail to 
be a just medium of comparison. It might happen, 
by chance, that these two parts should be the same, 
but it would be only by chance; in the general case 
they would be different parts, and if we choose to 
regard each part as a distinct term, we should again 
run into the error of having four terms instead of 
three; thus 

Some quadrupeds are cows, 

Some quadrupeds are sheep, 
Therefore Some sheep are cows. 

White is a colour, 
Black is a colour, 
Therefore Black is white. 

But if one of the extremes be compared with the 
whole of the middle term, and the other be compared 
only with a part, which part is necessarily contained 
in the whole, they may then be compared with each 
other. 

VI. Illicit process. 

Again, in order to distribute either the major or 
minor term in the conclusion, it must have been pre- ! 
viously distributed in the premiss in which it occurs ; 
because, we only have a right to compare that part 
of the term with the other, in the conclusion, which 









THE SYLLOGISM. 






115 


we 


have 


already 


compared with the middle in 


the 


premiss, 


thus 




CK 


- c 










All men are animals, 


b ~ 


o^ 










No dogs are men, 


i - 


C 








Therefore No dogs are animals. 









The technical name for this logical fallacy is the illicit 
process. In the example, the major term, animals, 
which is not distributed in the premiss (as it is 
the predicate of an affirmative proposition) is distri- 
buted in the conclusion (as the predicate of a nega- 
tive proposition) ; this is called an illicit process of the 
major term : if it be the minor term thus treated, it 
is called an illicit process of the minor term. 

The following is an example of illicit process of 
the minor. 

1. All men are rational beings, 

2. All men are animals, 

3. All animals are rational beings. 

In this example the minor term animals, which is un- 
distributed in the minor premiss — as the predicate of 
an affirmative proposition, — is distributed in the con- 
clusion, being there the subject of a universal. 

Let it be remembered that this is called an illicit 
process of the major or minor term, not of the major 
or minor premiss. 

VII. If both premisses in a syllogism be particular 
propositions, we can draw no conclusion ; thus : 

1. Some men are wise, 

2. Some men are foolish, 



116 LOGIC. 

leads us to no conclusion. Nor are we benefited if 
we make one of the premisses 'particular negative; 
thus : 

1. Some men are "wise, 

2. Some men are not brave, 

we are as before without any medium of comparison. 

The fact is as stated ; the causes are various, and 
will be fully explained in the chapter on Figure. 

It is sufficient, now, for the student to know that 
the cause is in every case, either an undistributed 
middle, or an illicit process of one of the other terms. 

By the foregoing axioms and rules, we extend the 
range of syllogistic forms, and are able to see the 
validity or invalidity of an argument without reducing 
it to the invariable formula of Aristotle's dictum. 
We proceed now to show how many of these forms 
there may be, and the relation they sustain to the 
dictum itself; and this brings us to the subject of 
Figure and Moods. 



FIGURE AND MOODS. 



CHAPTER VIII. 

OF FIGURE AND MOODS. 

(37.) Figure. 

figure is the technical name employed to designate 
the classification of syllogisms according to the posi- 
tion of the middle term with reference to the two ex- 
tremes in the premises. Now, it is evident that the 
middle term can have only four variations of position, 
and hence we say there are four figures. 

1st. The middle term may be the subject of the 
major premiss, and the predicate of the minor, and 
this designates the 1st figure. 

2d. It may be the predicate of both premisses, and 
thus the 2d figure is designated. 

3d. In the 3d figure it is the subject of both pre- 
misses ; and 

4th. In the 4th figure (which is the reverse of the 
1st), it is the predicate of the major premiss and the 
subject of the minor. 

If we designate the major term by P (as it is 
always the predicate of the conclusion), the minor 



118 LOGIC. 

term by S (being the subject of the conclusion), and 
the middle term by M, and merely state these various 
positions of the middle term, without considering or 
denoting the quantity or quality of the propositions in 
the syllogism, we shall have the abstract syllogisms, 



I. 


II? 


III. 


IV. 


M is P. 


P is M. 


M is P. 


Pis M. 


S is M. 


S is M. 


M is S. 


M is S. 


S is P. 


S is P. 


S is P. 


S is P. 



These are called the four figures ; and to the syllo- 
gisms which occur in them, the axioms and rules 
already laid down directly apply. 

If now we proceed to examine these figures in order, 
we shall find that the first figure is but the symbolical 
representation of Aristotle's dictum, the simplest form 
of the syllogism. There will be four variations of 
it : viz. : — 



1. 


2. 


3. 


4. 


All M is P. 


All M is P. 


No M is P. 


No M is P. 


All S is M. 


Some S is M. 


All S is M. 


Some S is M. 


All S is P. 


Some S is P. 


No S is P. 


Some S is not P. 



We have simply supplied the quantity and quality 
required. 

Since, in the major premiss, then, of Aristotle's 
dictum, we assert or deny the predicate of the whole 
class which is the subject (All M), it is evident that in 
the first figure, the major premiss is always universal. 
If, then, with this relative position of the middle term, 
i, e. in the first figure, we find a syllogism, the major 



FIGURE. 119 

premiss of which is particular, we may at once declare 
it to be invalid. 

Again, since the province of the minor premiss in 
the dictum is always to assert that certain individuals 
belong to the given class (and in no case to deny it), 
it appears that in the first figure the minor premiss 
must always be affirmative, so that if we find a syllo- 
gism in this figure with a negative minor premiss, we 
may at once declare it invalid. 

Thus, in stating the four forms of the dictum, we 
have stated the only four forms which the first figure 
can cover. 

But the other figures, which are not directly in the 
form which the dictum assumes, instead of being ex- 
plained by it, are to be considered in the light of the 
axioms and rules for determining the validity of syllo- 
gisms when the dictum does not directly apply. By 
examining the second figure, 

P is M, 
S is M, 

SisP, 

we shall find that there are several forms which it 
will assume when we supply the quantity and quality 
to the propositions. We observe at once that the 
conclusion must, in every case, be negative, because 

1st. The middle term is the predicate of both pre- 
misses ; 

2d. The middle term must be distributed at least 
once in the syllogism ; 



120 LOGIC. 

3d. In order that the predicate of a proposition 
shall be distributed, the proposition must be negative ; 

4th. This will give us one negative premiss, and by 
the second axiom, if we have a negative premiss the 
conclusion must be negative {universal or particular). 

Third Figure, 

M is P, 
M is S, 
Sis P. 

By the supplying of quantity and quality this 
figure assumes a greater variety of forms than any 
other. 

By considering the position of the terms here, it 
will appear that we can only draw particular conclu- 
sions. For if both premisses be affirmative, and we 
draw a universal conclusion, or All S is P, then S 
(the minor term) which was undistributed in the minor 
premiss (being the predicate of an affirmative propo- 
sition), will be distributed in the conclusion, as the 
subject of a universal ; or we shall have an illicit pro- 
cess of the minor. 

If the major premiss be negative, and we draw a 
universal conclusion, it is easily shown that the same 
error — an illicit process of the minor — obtains ; and 
if the minor premiss be negative, we shall have an 
illicit process of the major. 



MOOD. 121 

Fourth Figure. 

Pis M, 

M is S, 
Sis P. 

The fourth figure, which was not proposed by Aris- 
totle with the other three, and only recently adopted 
by logicians, is an inversion of the first, and an un- 
natural and unnecessary form of the syllogism. By 
a similar examination of all the terms we shall find, 
that we may draw, as conclusions, in this figure all the 
categorical propositions except A, which, as has been 
shown, can only be drawn in the first figure. It is 
the prerogative of Aristotle's dictum alone, to draw 
from certain premisses a universal affirmative con- 
clusion. 

The various forms of the syllogism due to the dif- 
ferent quantity and quality of the propositions compos- 
ing them, are arranged, in the different figures, in 
what are called moods, or a concise manner of ex- 
pressing a syllogism by symbols. - 

(38.) Of Mood. A f Q 

If, having any syllogisms, as the following — 

f All A is B, (A.) (NoAisB. (E.) 

1. I All C is A, (A.) 2. ) Some C is A. (I.) 

( All C is B, (A.) ( Some C is not B. (0.) 

we write together the symbols characterizing each 

proposition which composes them, we are said to deter- 

11 



122 LOGIC. 

mine the mood of the syllogism ; thus the symbol of 
the major premiss in the first syllogism is 

A, or universal affirmative ; 
that of the minor, 

A, or universal affirmative ; 
and that of the conclusion likewise 

A, or universal affirmative. 

Hence we say that A A A is the mood of the syllogism. 

In the second syllogism we shall find by a similar 
process that the mood is E I 0. 

Now, it is evident that the number of moods we 
can have will depend upon, 1st, the number of propo- 
sitions in the syllogism, viz., three ; and 2d, upon the 
number of categorical propositions which we can enu- 
merate, viz., four, A, E, I, ; it becomes then a 
simple algebraic arrangement of four letters A, E, I, 
0, in three columns in every possible combination. The 
number of these possible combinations will be sixty- 
four. For each of the propositions A, E, I, and 0, 
may be a major premiss ; and each of these may have 
each in turn as a minor premiss ; thus, 

Maj. prem. Maj. prem, Maj. prem. Maj. prem. 
A E I 

., i ill ill - ] Pill i i i i 

may have as mi- C A E I AEI0 AEI0 AEI0 

u or premisses, 5 

Again, each of these sets (sixteen in all) may have 
four different conclusions, i. e. each of the categori- 



MOOD. 123 

cals as a conclusion. Taking the first set, for example, 
and supposing the operation performed for the rest, 

FIRST SET. 
Maj. prem. A. 

f~~ T" ~~ 1 I 

Mm. prem. AEIO 



I I I I I I I I I I I I I I I I 

Cond, AEIO AEIO AEIO AEIO 

This same process may be performed for E, I, and 0. 
There will evidently be sixty-four moods, of which, 
however, it is at once evident that very many will 
violate the axioms and rules already laid down, and 
must be for this reason discarded. 

Thus, all the combinations of affirmative premisses 
having negative conclusions, as A A E, A I 0, &c, 
&c, must be thrown aside, because they violate the 
first axiom. 

All the sets of negative premisses, with whatever 
conclusions, are useless, as E E, 0, E 0, E, &c. 

All the sets of particular premisses, with whatever 
conclusions, must be neglected, such as 1 1, 0, I, 
I 0, &c. 

If all these eliminations be performed, and simple 
as they are, the student is advised to go carefully 
through them once for himself, we shall find twenty- 
eight moods excluded on account of negative and par- 
ticular premisses .: eighteen by the condition that the 
conclusion follows the inferior part, and we shall see 



124 LOGIC. 

that one — I E — is rejected for an illicit process of 
the major term, in every figure, and finally that of 
the sixty-four arrangements which we call moods, only 
eleven represent valid arguments, or 



AFFIRMATIVES 


and 


SEVEN NEGATIVES. 


AAA 




E 


A 


E 


All 




A 


E 


E 


A A I 




E 


A 





I A I 




A 















A 









E 


I 









A 


E 






If now we apply "these moods to each figure, in 
detail, it would seem, since there are four figures, that 
we should have 4 X 11 = 44 moods in all the figures, 
but in this application we find that many moods which 
are valid in one figure, are not in others ; as, for ex- 
ample, the mood I A I, which is allowable in the third 
figure, would be in the first figure a case of undis- 
tributed middle, and would further violate the prin- 
ciple of Aristotle's dictum, which requires that the 
major premiss should be a universal proposition. 
A E E is a valid mood in the second figure, while, in 
the first, it would have an illicit process of the major 
term, and would further violate that principle of the 
dictum which requires the minor premiss to be always 
affirmative. 

By applying these eleven moods to the four figures, 
we find that there would be six in each figure, or 



MOOD. 125 

I 

twenty-four in all ; but even of these, five are omitted 
as useless ; for example, the mood A A I, in the first 
figure, because it is implied and contained in the 
mood AAA. Since, if the universal conclusion A 
be true, the particular I is necessarily true. By an 
application of each of these moods to every figure, 
we shall have left, finally, nineteen moods in all ; or, 
four in the first figure, four in the second, six in the 
third, and five in the fourth. 

The moods of the first figure are called perfect 
moods ; those in the other figures, imperfect moods. 

As it has been asserted that all arguments may be 
put in the form of Aristotle's dictum, that is, that 
all the imperfect moods may be made perfect, we pro- 
ceed to fulfil this assertion, by the process of reduction, 
i. e. the reducing of moods in the 2d, 3d, and 4th 
figures to the 1st figure, which is the form of the 
dictum. 
V In order to facilitate this process, as well as to re- 
I tain easily in the memory the different moods and 
their value, the following verses, Latin in sound and 
scansion, but without intrinsic meaning in the words, 
have been formed : — 

Fig. I.— BArbArA, CElArEnt, DArll, FErlO, date-primce. 
Fig. II.— CEsArE, CAmEstrEs, FEstlnO, FAkOrO, tmundce. 

Fig III I Tertia DArA P tI ' MsAmls, DAtlsI, FElAptOn, 
\ DOkAmO, FErlsO, habet ; quarto, insuper addit. 
Fig. IV.— BrAmAntIP, CAmEnEs, DImArls, FEsApO, FrEsIsOn. 
11*- 



126 LOGIC. 

There are variations in these lines, made by various 
writers ; we have adopted the above as the form which 
will indicate to us in the simplest manner the pro- 
cesses of Reduction. 

Before explaining these lines, which the student 
must memorize in order to make them useful, that he 
may have the moods, and their places in the figures, 
at his tongue's end, it will be observed that there are 
a few words used in these verses which are of no use 
except to make out the hexameter lines ; of these are 
dato primce in the first, secundoz in the second, tertia 
habet in the third, and quarta insuper addit, which 
states — moreover the fourth adds, &c. Leaving these 
out of the consideration, in the lines themselves the 
vowels in each word represent the moods ; thus, Bar- 
bara is the mood AAA; Cesare, the mood JE A JE, 
&c, &c. 

The following consonants indicate what changes 
are to be made in the given imperfect mood to reduce 
it to a perfect mood of the first figure : — s, that the pro- 
position indicated by the vowel immediately preced- 
ing it is to be converted simply ; thus in Camestres, the 
first s indicates the simple conversion of the first JE, 
or the minor premiss, and the last s the simple con- 
version of the second JE, or the conclusion. In simi- 
lar relations p and h stand respectively for conver- 
sion by limitation and conversion by negation; m, 



MOOD. 127 

wherever it occurs, expresses that the premisses must 
be transposed ; the other consonants have no mean- 
ing, and are only employed to frame the words. P, 
in the mood Bramantip of the fourth figure, denotes 
that the transposed premisses, indicated by m, will 
warrant a universal conclusion instead of a particular. 
The initial letters B, C, D, F, of the words which 
contain the moods, are so arranged throughout the 
figures as to indicate the mood in the first figure to 
which any imperfect mood will be reduced; thus 
Darapti of the third figure will, when reduced, 
become Darii of the first, Oamestres will become 
Celarent, &c. 

It must be observed that this arrangement is only 
for the sake of convenience, as the process of reduc- 
tion is invariable, and the mood Darapti would become 
when reduced the mood A 1 1 of the first figure, whether 
it were called Darii or by some other name. Stu- 
dents are apt to be misled with reference to these ini- 
tial letters, and to suppose that they will aid them in 
the process of reduction ; it is on this account that 
they are cautioned that this is only a convenient and' 
not an auxiliary arrangement. Before proceeding to 
explain the system of reduction, let us give an ex- 
ample of each mood, in all the figures ; putting the 
logical frame-work to its legitimate use, and showing 
every form which the syllogism can assume. We shall 



128 LOGIC. 

make the examples very simple, leaving it to the stu- 
dent, with these before him, to frame longer and more 
complex ones for himself ; a practical exercise which 
will be found very useful. The middle term is placed 
in italics in each example. 

Examples. 

FIGURE I. 

Barbara. 

A. Every desire to gain by another's loss is cove- 
tousness. 

A. All gaming is a desire to gain by another's loss. 
A. All gaming is covetousness. 

Celarent. 

E. No one who is enslaved by his appetites is free. 
A. Every sensualist is one who is enslaved by his 
appetites. 
E. No sensualist is free. 

Darii. 

A. All pure patriots deserve the rewards of their 
country. 

I. Some warriors are pure patriots. 

I. Some warriors deserve the rewards of their 
country. 



EXAMPLES IN THE FOUR FIGURES. 129 

Ferio. 

E. Nothing which impedes commerce is beneficial 
to the revenue. 

I. Some taxes impede commerce (or are things which 
impede commerce). 

0. Some taxes are not beneficial to the revenue. 

FIGURE II. 

Oesare. 

E. No vicious conduct is praiseworthy. 

A. All truly heroic conduct is praiseworthy. 

E. No truly heroic conduct is (or can be) vicious. 

Camestres. 

A. Every true philosopher accounts virtue a good 
in itself. 

E. No advocate of pleasure accounts virtue a good 
in itself. 

E. No advocate of pleasure is a true philosopher. 

The true middle term here would be (one who) 
accounts virtue a good in itself. 

Festino. 

E. No righteous acts will produce ultimate evil to 
the actor. 

1. Some kinds of association will produce ulti- 
mate evil to the actor. 

I 



130 • LOGIC. 

0. Some kinds of association are not righteous 
acts. 

Fakoro. 

A. All true patriots are friends to religion. 

0. Some great statesmen are not friends to religion. 

0. Some great statesmen are not true patriots. 

FIGURE III. 

Darapti. 

A. All wits are dreaded. 
A. All wits are admired. 

1. Some admired (persons) are dreaded. 

Disamis. 

I. Some lawful things are inexpedient. 

A. All laivful things are what we have a right 
to do. 

I. Some things which we have a right to do are 
inexpedient. 

Datisi. 

A. All that wisdom dictates is right. 

I. Something that wisdom dictates is amusement. 

I. Some amusement is right. 

Felapton. 

E. No science is capable of perfection. 
A. All science is worthy of culture. 



EXAMPLES. 131 

0. Something worthy of culture is not capable of 
perfection. 

Dolcamo. 

0. Some noble characters are not philosophers. 
A. All noble characters are worthy of admiration. 

0. Some (who are )worthy of admiration are not 
philosophers 

Feriso. 

E. No false theories exist in a perfect state of 
being. 

1. Some false theories are harmless things. 

0. Some harmless things do not exist in a perfect 
state of being. 

FIGURE IV. 

Bramantip. 

A. All oaks are trees. 

A. All trees are vegetables. 

1. Some vegetables are oaks. 

Qamenes. 

A. All miracles are things of rare occurrence. 

E. No things of rare occurrence make a slight im- 
pression on the mind. 

E. No (things which) make a slight impression on 
the mind are miracles. 



132 LOGIC. 

Dimaris. 

I. Some taxes are oppressive. 

A. All (that is) oppressive should be repealed. 

I. Some things which should be repealed are taxes. 

Fesapo. 
E. No immoral acts are proper amusements. 
A. All proper amusements are designed to give 
pleasure. 

0. Some (things) designed to give pleasure are not 
immoral acts. 

Fresison. 

E. No acts of injustice are proper means of self- 
advancement. 

1. Some proper means of self-advancement are un- 
successful. 

0. Some unsuccessful (efforts) are not acts of in- 
justice. 

It will be observed that the conclusions in the fourth 
figure are indirectly stated, and that it would seem as 
if in tracing the major term back from its place as 
predicate of the conclusion, it is in reality predicated 
by means of the other terms of itself ; thus : in the 
conclusion it is predicated of the minor, which in the 
minor premiss is predicated of the middle, which in 
the major premiss is predicated of the major. The 
fourth figure, therefore, is not often used, and is 



MOOD. 133 

rather accidentally stumbled into than employed in- 
tentionally. 

The exact accordancy of the first figure with the 
dictum of Aristotle has been already stated. Of the 
second figure, it may be remarked that it is commonly 
used to disprove something that has been maintained, 
or is likely to be believed, although not true. As an 
illustration, suppose it had been asserted that 

All great statesmen are true patriots. 

Then our example just given of Fakoro would be a 
refutation of this, and the argument would naturally 
take that form. 

Of the third figure, it will appear that it will be 
useful where we have singular terms, which can only 
be subjects of propositions, i. e. never predicates ; and 
also where our purpose is to offer and sustain an ob- 
jection to our opponent's premiss, which is particular 
when the argument requires it to be universal. 

There are very many inverted and curious forms 
of arguments growing out of the elliptical and in- 
verted forms of propositions, which we have already 
considered. Two common examples of these are 
added by way of illustration. 

1. 

None but whites are civilized. 

The Hindoos are not whites. 

The Hindoos are not civilized. 

The phrase none but whites, may be rendered, other 

12 



7- 



134 LOGIC. 

than whites ; and this being the true middle term, we 
shall have — 

No other than whites are civilized. 
All Hindoos are other than whites. 
No Hindoos are civilized. 

Which is evidently a syllogism in Oelarent, of the first 
figure. 

2. 
No one is rich who has not enough. 
No miser has enough. 
No miser is rich. 

The major and minor premisses must be put in the 
form of categorical propositions, and we shall have 

No one who has not enough is rich. 
Every miser is one who has not enough. 
No miser is rich. 

Which is likewise in the mood Oelarent. In both these 
examples the minor premiss, which appears to be a 
negative proposition, is in reality affirmative. 

(39.) Of Reduction. 

If we have any imperfect mood, i. e., a mood in 
the second, third, or fourth figure, and we desire to 
prove the same conclusion in the first figure, so that 
the dictum of Aristotle may immediately be applied 
to it; the process by which this is done is called 
Reduction. 

Reduction is of two kinds, direct and indirect. 
Direct reduction consists in proving in a perfect mood 
either the same conclusion, or one which, being illa- 
tively converted, will give us the same conclusion which 



REDUCTION. 135 

we had in the imperfect mood. Indirect reduction con- 
sists in proving, not that the original conclusion is 
true, but that its contradictor!/ is false, from which — 
by the scheme of opposition (30) — we know that the 
original conclusion must be true. 

Of direct reduction. 

It has been shown that we have a right to convert 
any of the propositions of the syllogism illatively ; 
and it is also evident that we may transpose the pre- 
misses without affecting the truth of the propositions 
or the validity of the argument. If, then, we apply 
the processes indicated by the letters in the mnemonic 
lines, we shall see that they will give us the forms of 
direct reduction. 

Taking for example Cesar e, the mood EAE in 
the second figure ; to write it out we remember in the 
*irst place that the position of the middle term in the 
second figure is predicate of both premisses, and we 
observe that the major premiss is E, universal negative, 
the minor premiss A, universal affirmative, and the 
conclusion E, universal negative : we have, then, X 
being the major, Z the minor, and Y the middle term, 





Cesare. Fig. II. 


E. 


No X is Y = No men are trees. 


A. 


All Z is Y == All oaks are trees. 


E. 


No Z is X = No oaks are men. 



The only consonant in the word CEsArE which in- 
dicates a process of reduction is s, which tells us that 



r- 



-^ 



136 LOGIC. 

the major premiss, expressed by the first E, is to be 

simply converted ; performing this operation we shall 

have 

Celarent. Fig. I. 

E. No Y is X = No trees are men. 
A. All Z is Y = All oaks are trees. 
E. No Z is X = No oaks are men. 

This syllogism is in the first figure, since the mid- 
dle term Y or trees, has become the subject of the 
major and the predicate of the minor premiss ; again, 

Fakoro. Fig. II. 

A. All X is Y = All good men are virtuous. 

0. Some Z is not Y = Some clergyman are not virtuous. 

0. Some Z is not X = Some clergymen are not good mem 

The k expresses that the major premiss (A) is to be 
converted by negation; performing this operation, 
(there is no other indicated), we shall have 

Ferio. Fig. I. 

E. All (not Y) is not X == All (not virtuous) are not good men. 
I. Some Z is (not Y) = Some clergymen are (not virtuous). 
0. Some Z is not X = Some clergymen are not good men. 

This process, in effect, changes our middle term 
from Y or virtuous to [not Y) or [not virtuous), while 
we have the same conclusion as before in the mood 
Ferio, of the first figure. 

The reduction of the other moods of the second 
figure will be analogous to those already performed, 
and the student will find no difficulty in reducing 
them for himself. Passing then to the third figure, 



DIRECT REDUCTION. 137 

and remembering that in this figure the middle 
term is the subject of both premisses, let us reduce 

the mood 

Disamis. Fig. III. 
I. Some Y is X = Some men are heroes. 
A. All Y is Z = All men are mortal. 
I. Some Z is X = Some mortals are heroes. 

The two letters which indicate changes in the pro- 
cess of reducing this mood are s (twice employed) and 
m: s indicates the simple conversion of the major 
premiss and the conclusion, and m, the transposition 
of the premisses ; performing these operations, we have 

Darii. Fig. I. 
A. All Y is Z = All m*n are mortal. 
I. Some X is Y = Some heroes are men. 
I. Some X is Z = Some forces are mortal. 

which conclusion is the simple converse of the original 
conclusion, as was indicated by the £i?^l s. 

Fesapo. Fig. IV. 
E. No X is Y = No quadrupeds are m<°i*. 

A. All Y is Z = All men are animals. 

0. Some Z is not X = So*»e animals are not q^i-MMpeds. 

Converting the major premiss simply, and the minor 

premiss by limitation, as indicated by the s and p, we 

shall have 

Ferio. Fig. I. 
E. No Y is X = No men are quadrupeds. 

1. Some Z is Y = Some animals are men. 

0. Some Z is not X = Some animals are not quadrupeds. 

It will be well for the student to reduce every im- 

12* 



138 



LOGIC. 



perfect mood, forming for himself particular ex- 
amples under each. 

Although we have made the subject of Reduction 
plain by the examples already given, we append a 
table of the manner of reducing each mood for refer- 
ence, until the student is familiar with them. It is 
but a recapitulation in tabular form of what has been 
already explained. 



Mood to be reduced. 



Will re- 
duce to. 



Process of reduction. 



Fig. II. 



Cesare. 

Camestres. 

Festino. 
I Fakoro. 



f Darapti. 

j Disamis. 

Fig. III. i DatisL 

Felapton. 

Dokamo. 
[ Feriso. 

CBramantip. 
I Camenes. 
Dimaris. 



Fig. IV. -{ 



Fesapo. 
Fresison. 



Celarent. 

Celarent. 

Ferio. 
Ferio. 

Darii. 

Darii. 

Darii. 
Ferio. 

Darii. 
Ferio. 

Barbara. 
Celarent. 
Darii. 

Ferio. 

Ferio. 



(s) Convert major premiss simply. 

(m) Transpose the premisses, (s & s) 
Convert the minor premiss and con- 
clusion simply. 

(s) Convert the major premiss simply. 

(k) Convert the major premiss by ne- 
gation. 

(p) Convert the minor premiss by 
limitation. 

(m) Transpose the premisses, (s & s) 
Convert the minor premiss and con- 
clusion simply. 

(s) Convert the minor premiss simply. 

(p) Convert the minor premiss by 
limitation. 

(k) Convert the major premiss by ne- 
gation, (m) Transpose the premisses. 

(s) Convert the minor premiss simply. 

(m) Transpose the premisses, (p) Con- 
vert the conclusion by limitation. 

(m) Transpose the premises, (s) Con- 
vert the conclusion simply. 

(m) Transpose the premisses, (s) Con- 
vert the conclusion simply. 

(s) Convert the major premiss simply, 
(p) Convert the minor premiss by 
limitation. 

(s <fe s) Convert the major and minor 
premisses simply. 



INDIRECT REDUCTION. 139 

(40.) Indirect Reduction. 

This process, called by the old logicians Beductio 
ad impossibile, is analogous to the reductio ad absur- 
dum of geometry. It consists in proving that the 
given conclusion cannot be false, by proving, in the 
first figure, that its contradictory is false. 

The symbols used to indicate the processes of 
direct reduction, do not guide us in the indirect re- 
duction, but we must deduce rules for this apart from 
the other. 

To illustrate, let us take the mood 

Fdkoro. Fig. II. 

A. All X is Y = All good men are virtuous. 

0. Some Z is not Y = Some clergymen are not virtuous. 

0. Some Z is not X = Some clergymen are not good. 

If this conclusion be not true, its contradictory All Z 
is X = All clergymen are good, must be true. Assum- 
ing this as true, and taking it in the place of the 
minor premiss in the syllogism, we shall have a new 
syllogism, as follows : — 

A. All X is Y = All good men are virtuous. 
A. All Z is X = All clergymen are good men. 

from which premisses by our rules we draw the con- 
clusion 

A. All Z is Y = All clergymen are virtuous. 

But this conclusion must be false, because it is the 
contradictory of the original minor premiss, — and the 



140 LOGIC. 

premisses were assumed to be true, — hence one of 
these last premisses from which this conclusion is 
derived must be false ; but it is not the major, for 
that was one of the originally assumed premisses ; it 
must, therefore, be the minor, which we know to be 
the contradictory of our original conclusion ; and the 
original conclusion must therefore be true: this, it 
will be observed, is proven in the first figure, in the 
mood Barbara, To take another example, let us re- 
duce the mood 

Darapti. Fig. III. 

A. All Y is X = All gold is precious. 

A. All Y is Z = All gold is a mineral. 

I. Some Z is X = Some mineral is precious. 

If this conclusion be not true, then must its contra- 
dictory 

No Z is X = No mineral is precious, 

be so. Substituting this as the major premiss in the 
syllogism, we have 

No Z is X = No mineral is precious. 
All Y is Z = All gold is a mineral. 

From which we draw the new conclusion 

No Y is X = No gold is precious. 
But this conclusion is false, because it is the contrary 
of the original major premiss, which we assume to be 
true ; one of the premisses from which it was derived 
must be therefore false : it cannot be the minor, which 
was also assumed to be true ; it must, therefore, be 



INDIRECT REDUCTION. 141 

the major, which is the contradictory of the original 
conclusion; hence, the original conclusion must be 
true. 

It will occur, in reducing many of the moods by 
this process, as in the last example, that we shall find 
the conclusion false because it is the contrary and not 
the contradictory of one of the original premisses. 
By referring to the subject of Opposition (30), we see 
that if one contrary is true the other must be false. 

Without presenting a greater number of examples 
of this kind of reduction, which the student may 
multiply for himself, we lay down the following rules 
for reducing the various imperfect moods. 

Rules for Indirect Reduction. 

1st. In the second figure, substitute the contradic- 
tory of the conclusion for the minor premiss, and pro- 
ceed as above in the mood Fahoro. 

2d. In the third figure, substitute the contradictory 
of the conclusion for the major premiss, and proceed 
as with the mood Darapti. 

3d. In the fourth figure, substitute the contradictory 
of the conclusion for the minor premiss, and proceed 
as before. 

As reference is always easier to a tabular form, we 
annex one showing in what perfect mood the indirect 
reduction of each imperfect mood will take place : — 



142 



LOGIC. 



Fig. II. 


Fig. III. 


Fig. IV. 


Cesare to Ferio. 


Darapti to Celarent. 


Bramantip to Celarent. 


Camestres to Darii. 


Disamis to Celarent. 


Camenes to Darii. 


Festino to Barbara. 


Felapton to Barbara. 


Dimaris to Celarent. 


Fakoro to Barbara. 


Datisi to Ferio. 


Fesapo to Celarent. 




Dokamo to Barbara. 


Fresison to Celarent. 




Feriso to Darii. 





Before proceeding to consider the irregular, infor- 
mal, and compound syllogisms, we pause to show the 
method of geometrical notation, already referred to, 
by which the pure syllogism may be expressed. 

(41.) Notation of the Syllogism. 

As there subsists in the mathematics such a rela- 
tion of analysis to geometry, as that most analysis 
is capable of geometrical construction, and every form 
of geometry may be stated analytically in terms of 
its equation ; so mathematical logicians have attempted 
to make for the analysis or symbolic form of the syl- 
logism such a geometrical notation as shall at a glance 
represent to the eye, in areas of limited space, what 
the symbols do to the mind. Indeed, the idea is so 
simple that we have already illustrated the dictum of 
Aristotle through its agency. Many writers, however, 
have been inclined to go too far in its use. 

The schemes of notation best known are those of 
Euler, Ploucquet and Lambert, and the more com- 
plete one of Sir William Hamilton. This latter, how- 
ever, passing beyond our needs, is suited to such 



NOTATION. 143 

changes as would result from the introduction of the 
new analytic, and, as we have advisedly declined to 
place that system in our text-book, it is sufficient to 
mention Sir W. Hamilton's scheme without explain- 
ing it. In a more extended historical treatise it 
would demand a special consideration. "We can here 
only explain what we mean to use. 

Euler's scheme of notation is altogether the one 
best suited to our purpose, and we shall limit our- 
selves to the explanation of that. It is essentially an 
arrangement of three circles, to represent the three 
terms of a syllogism, and, by their combination, the 
three propositions. Thus if we have the judgment 

All men are mortal, 

we know that under this class, all men, are included 
many species and individuals ; as, for example, all 
Americans. Representing then the sphere of the 
conception mortal, by a circle; placing within this 
circle a smaller one, wholly contained in it, as the 
sphere of all mew, 'and yet a smaller one wholly con- 
tained in this latter, as the sphere of all Americans, 
we shall have 




144 



LOGIC. 



which is the notation of a syllogism in BArbArA. 
By similarity of process, we shall represent the syllo- 
gism in CElArEnt 

No A is B, 

All C is A, 

No C is B. 




DArll, will be thus expressed : — 




All A is B, 
Some C is A, 
Some C is B. 



Here it is evident that it is only that some which is 
contained in A that we have a right to assert is also 
contained in B, although other portions of C may by 
chance be also contained in B. 

FErlO :— 

No A is B, 
Some C is A, 
Some C is not B. 

(2) 





NOTATION. 



145 



Here two cases are presented ; where no C is B, and 
where some C is B ; neither of which affects the truth 
of the conclusion that some is not B. We have 
only applied this scheme to the first figure, but by 
this simple notation of Euler every syllogism in the 
other figures may be represented to the eye, and made 
clear to those who are much quicker at geometry than 
at analytical work. Take for example Darapti of 
the third figure : — 

All A is B, 
All A is C, 
Some C is B. 



But besides this representation of valid syllogisms, 

this system exposes at once fallacious arguments and 

acts as a test upon a test of their unsoundness. Take 

for example the case of illicit process of the major 

term : — 

All quadrupeds are animals, 
A bird is not a quadruped, 
A bird is not an animal. 





In which the figure denies the conclusion by allowing 
the premisses, and yet showing that birds are contained 



13 



K 



140 LOGIC. 

under the genus animal. Or if we take the case of 
negative premisses : — 

No A is B, 
No C is A, 




the figure shows us that there is no relation whatever 
established between or among the terms which would 
entitle us to a conclusion. . 

The student will find it easy and pleasant to write 
out all the moods and the logical fallacies by this cir- 
cular method of notation ; and, as two modes of coming 
at facts make the memory more tenacious of them, 
this practice will fix clearly in his mind the moods 
and figures of the syllogism. 

This system also illustrates the categorical proposi- 
tions as to the distribution of their terms, very satis- 
factorily : 

AH A is B, 
No A is B, 
Some A is B, 

Some A is not B. 

' It would be a good exercise for the student to be called 
upon to represent any given syllogisms by this notation. 




ABRIDGED SYLLOGISMS. 147 



CHAPTER IX. 

OF IRREGULAR, INFORMAL, AND COMPOUND ARGU- 
MENTS. 

(42.) Of Abridged Syllogisms, 

We have thus far considered only those arguments 
which appear directly and without analysis in the 
form of a simple syllogism ; and have explained those 
processes which we perform upon known and acknow- 
ledged facts, stated as premisses and conclusion ; but 
the mind of man sometimes passes intuitively over 
certain steps of these processes without stopping to 
express them, which gives rise to abridged arguments ; 
or it halts in doubt and uncertainty, being not sure 
of its facts, but frequently balancing between two, 
one of which must be true, because of the truth or 
falsity of the other. This produces hypothetical 
syllogisms. 

All these in the present chapter will be treated of 
as informal syllogisms, or arguments which are not 



148 LOGIC. 

syllogisms in form, but which, if they be valid, must 
be capable of being put into the syllogistic form. 

The first of the abridged arguments to be con- 
sidered, because the one in most common use, is 

The Enthymeme* 
The enthymeme is a syllogism with one premiss sup- 
pressed ; it matters not which ; thus, having the syl- 
logism, 

All men are mortal, 

Caesar is a man, 

Caesar is mortal, 

we may suppress the major premiss and write the 

enthymeme, — 

Caesar is a man. 
Therefore Caesar is mortal. 

Or suppressing the minor premiss, we have, 

All men are mortal, 
Therefore Caesar is mortal, 

either of which is a satisfactory expression, because 
all three terms of the syllogism are expressed in either 
form of the enthymeme, and we can at once recon- 
struct the syllogism ; thus, taking the latter form, 
with the minor premiss suppressed', we see by examin- 
ing the conclusion, in which the major and minor 
terms are always contained, that Ccesar is the minor, 
being the subject of the conclusion, and mortal the 
major, being the predicate. Men, then, must be the 

* EvOvneopcu, to conceive in the mind. 



THE ENTHYMEME. 149 

middle term, and we at once compare it with the 
minor term to form the suppressed premiss ; thus : 

Csesar is a man. 
By a similar process we may reconstruct the syllo- 
gism when the major premiss is suppressed. 

It is worthy of observation that in ordinary dis- 
course men suppress the major premiss habitually, as 
that to which the mind most readily yields assent, 
although if the proof of its truth be required, the 
task would be more difficult than to establish the truth 
of the minor. Thus, in the example given above, we 
would take for granted as a fact that 

All men are mortal ; 

whereas, without the declarations of the Bible — and 
Logic, as a science, moves independently of any ex- 
traordinary or supernatural dicta — this proposition is 
incapable of proof; for, although all men have died 
thus far in the world's history, the process of induc- 
tion cannot be finished until the end of man as a race. 

But this seems like a cavil. The major premiss, 
although thus incapable of mathematical proof, is the 
one which most surely demands belief; and so, when 
in the enthymeme we speak of the suppressed pre- 
miss, we mean the major premiss, unless it be other- 
wise explained. 

As a simple rule for reconstructing the syllogism 

from the enthymeme, we observe that, 
13 * 



150 LOGIC. 

If the subject of the conclusion be found in the 
expressed premiss, that premiss is the minor. If the 
predicate of the conclusion be found in the expressed 
premiss, it is the major. 

Sometimes it becomes necessary to put the enthy- 
meme into logical form before proceeding to recon- 
struct it. Thus, the example given above might be, 
and most commonly is, thus spoken or written : — 

Caesar is mortal, 
Because Caesar is a man. 

which is evidently a transposed form of the enthy- 
meme. Whenever the causal conjunction because 
unites the propositions of an enthymeme, we may in- 
vert the propositions and unite them with the illative 
conjunction therefore, and then proceed to reconstruct 
the syllogism, thus : 

Caesar is a man, 
Therefore He is mortal. 

Many abridged arguments which appear in a hypo- 
thetical form, are in reality simple enthymemes, thus : 

If murder is a crime, 

The murderer should suffer. 

In which there is really no hypothesis or condition in 

the premiss, because all allow that murder is a crime ; 

and are consequently ready to declare that 

The murderer should suffer. 

When the enthymeme has been reconstructed into a 



THE SORITES. 151 

syllogism in any one of the figures, we shall be able 
to put it directly into the first figure, and can then 
apply to it the test of Aristotle's dictum. 

ju (43.) The Sorites* or Chain Argument. ,f 
The Sorites is an abridged argument consisting of 
a series of propositions in which the predicate of the 
first is the subject of the second ; the predicate of 
the second the subject of the third, and so on until 
we combine the subject of the first and the predicate 
of the last to form a conclusion. Thus : — 

A is B = The mind is a thinking substance. 

B is C = A thinking substance is a spirit. 

C is D = A spirit has no composition of parts. 

D is E = (That which has) no composition of parts is indissoluble. 

E is F = (That which is) indissoluble is immortal. 



Concl. A is F = The mind is immortal. 

Now, if we try to put this collection of abridged 
arguments into the syllogistic form, in order to apply 
the dictum of Aristotle to them, we shall see that the 
Sorites is an abridgment of a series of syllogisms in 
the first figure ; that the terms B, C, D, and E, which 
are used twice, are middle terms, and that we may 
construct as many syllogisms as we have middle terms. 
Taking then the second proposition of the sorites, B 
is C y as the major premiss of the first syllogism ; and 

* o-copeirris = a heap, or collection. 

f Called by the Germans, more significantly, Kettenschluss, or chain 
argument. 



152 LOGIC. 

the first A is B, as the minor, we shall have as a con- 
clusion A is 0, which we use as the minor premiss of 
a second syllogism, using the third proposition of 
the sorites as a major premiss ; and so on, as long as 
the middle terms last, thus : — 



1st. 




2d. 


3d. 


4th. 


BisC, 




C is D, 


Dis E, 


Eis F, 


AisB, 




AisC, 


A is D, 


AisE, 


AisC. 




AisD. 


AisE. 


AisF. 


A thinking substance is 


a spirit. 




The mind 


is a 


thinking 


substance. 




The mind 


is a 


spirit. 







1st. 



A spirit has no composition of parts. 
2d. The mind is a spirit. 

The mind has no composition of parts. 

That which has no composition of parts is indissoluble. 
3d. The mind has no composition of parts. 
The mind is indissoluble. 

That which is indissoluble is immortal. 
4th. The mind is indissoluble. 
The mind is immortal. 

These are all in the first figure, and consequently are 
forms to which the dictum will directly apply. 

It must be observed that in the sorites the first pro- 
position, A is B, is the only one which may be 'particu- 
lar, because it is the only minor premiss expressed, 
every other being used as a major, and we have 
already seen that in the first figure the major premiss 
must be universal. 



THE SOKITES. 153 

So, again, the last proposition, E is F, is the only 
one that may be negative, for, if any other be nega- 
tive, we should have in one of the syllogisms a nega- 
tive conclusion which is to be in turn the minor pre- 
miss of the succeeding syllogism, and we have already 
shown that in the first figure the minor premiss must 
be affirmative. But the conclusion deduced from the 
last syllogism does not become a minor premiss, and 
so the last conclusion may be negative ; it would then 

read thus : 

No E is F. 
All A is E. 
No A is F. 

Or the chain of the sorites would be broken in what- 
ever place the negative proposition should occur. 

The sorites is a very simple and conclusive abridged 
form of argument ; for the mind, taking the only ex- 
pressed minor term A, which is expressed in the 
chain, links it by jumping from middle term to middle 
term, B, C, D, E, to the final major term or F, as 
surely and more easily, than in the syllogisms into 
which it is elaborated. 

By its aid we easily establish the points in any 
great argument, either as recapitulating the process 
of the argument, or as stating them preparatory to a 
comprehensive discussion. Thus, to establish the 
effect of a republican government, we shall have, 



154 LOGIC. 

The Americans make their own laws. 
Those who make their own laws are free. 
Those who are free are contented. 
Those who are contented are happy. 
Therefore The Americans are happy. 

It is evident that the sorites may be properly stated 
in the inverse order ; thus : 

D is E, C is D, B is C, A is B, 
Therefore A is E. 

Here the sorites starts from its widest terms, D 
and E, to include the narrower and more limited 
terms, C, B, and finally, A. 

This form is called the Q-oclenian Sorites, from the 
name of its originator. It serves, perhaps, better to 
illustrate the fact stated that only the most extensive 
proposition, which in the ordinary form is the last, and 
in this, the first, may be negative ; which, as we have 
seen, will give us a negative conclusion ; thus : 

D is not E, C is D, B is C, A is B, 
Therefore A is not E. 

Hypothetical Sorites. 

If we have a string of conditional propositions, 
such that the consequent of each becomes the ante- 
cedent of the succeeding one, the argument is called 
a hypothetical sorites, and the conclusion is obtained 
either by affirming the first antecedent with the last 



THE EPICHIKEMA. 155 

consequent, or by denying the last consequent with 
the first antecedent ; thus : 

1. If A is B, C is D ; If C is D, E is F ; 
But A is B, Therefore E is F. 

2. If A is B, C is D ; If C is D, E is F ; 

But E is not F, Therefore A is not B. 

Examples. 

1. 

If the Bible is from Grod it should be taught ; 

If it should be taught, men should be set apart to teach ; 

If men should be set apart to teach, they should be supported ; 

But the Bible is from God, therefore its teachers should be supported. 

2. 

If the Bible is false, it deceives the world ; 

If it deceives the world it should be destroyed ; 

But it should not be destroyed, therefore it is not false. 

To the hypothetical sorites it is evident that the 
Goclenian form will also apply. Indeed this is illus- 
trated in the last case mentioned, where we reason 
back from the denial of the last consequent to the 
denial of the first antecedent. 

(44.) Of the Ejpichirema* 

Most arguments employed in ordinary conversation 
and writing consist of simple syllogisms, abridged 
into enthymemes, linked together in a compound form ; 

* The Greeks seem to have considered this a great logical weapon, 
as the name they gave it signifies a violent onset, or laying of hands 
upon, tm, and xap. 



156 LOGIC. 

but in many cases the form of the syllogism is ob- 
served where the premisses are arguments in them- 
selves. When the premisses are thus separately 
established, before the conclusion is deduced, the 
argument is called an Epichirema ; thus : 

The victors are injured by war ; because it hardens their hearts ; 
The French were victors at Marengo, for they retained the field ; 
The French were injured by their victory. 

The major premiss is an enthymeme, which may be 
expanded into a syllogism ; the same is true of the 
minor ; hence we have two distinct arguments within 
the one which originally appeared. To apply the 
tests to their validity, they need only be written out 
in syllogistic form. In most apparently simple syllo- 
gisms, there is in reality implied the epichirema. As 
for example, in the one given to illustrate the mood 
Fakoro, of the second figure, 

All true patriots are friends to religion, 

Some great statesmen are not friends to religion, 

Some great statesmen are not true patriots, 

the major premiss demands in itself a reason. 
Thus: 

All true patriots are friends to religion, because religion is the basis 
of national prosperity and advancement. 

So also does the minor, 

Some great statesmen are not friends to religion, because their own 
lives are not in accordance with its precepts. 

Each of the premisses given is an enthymeme ; of 



HYPOTHETICAL SYLLOGISMS. 157 

which the clause because, $c, is the premiss, and the 
first statement, all true patriots, SfC, is the conclusion. 
]STow, this premiss to the premiss is called the pro- 
syllogism. 

Sometimes the establishment of the final conclu- 
sion will warrant us in drawing other conclusions 
also; thus: 

AisB, 

Cis A, 
Therefore C is B. 
Therefore X is Y, &c. 

This conclusion from a conclusion (X is Y) is called 
the epi-syllogism. 

To take the example before quoted, we shall have 

All true patriots are friends to religion. 
Some great statesmen are not friends to religion. 
Some great statesmen are not true patriots. 
Therefore They deceive their countrymen, 

and Deserve no rewards from their country, fyc. 

% (45.) Of Hypothetical Syllogisms. 

Corresponding to the various forms of hypothetical 
propositions, viz., conditional, causal, disjunctive, &c, 
we have conditional, disjunctive and causal syllogisms. 
They are all of so simple a nature that the mind 
finds no difficulty in the ratiocination which they ex- 
press ; but as we have asserted that, if valid, they 

may be reduced to the form of a categorical syllogism 
14 



158 LOGIC. 

in the first figure, we proceed to show how this may 
he done. 

Conditional Syllogisms. 
If we examine a conditional proposition we shall 
see at once that the affirmation of the consequent will 
follow from the affirmation of the antecedent ; thus : 

If A is B, G is!) = If he has a fever, he is side. 

But if we deny the antecedent, we may not therefore 
deny the consequent, since this consequent might 
spring from some other antecedent as well as from 
the one given. Thus : 

If A is not B, if he has not a fever, 

we cannot say, 

C is not D = he is not sick. 
since 

C might be D = he might be sick, 

from some other cause than 

A being B, or his having a fever. 

For similar reasons we may pass from the denial of 
the consequent to the denial of the antecedent, but 
not from the affirmation of the consequent to the 
affirmation of the antecedent. When we pass from 
the affirmation of the antecedent to the affirmation 
of the consequent, the reasoning is called constructive ; 
and when we pass from the denial of the consequent 
to the denial of the antecedent, it is called destructive. 

We may form, then, two, and only tivo, forms of 
conditional syllogisms, constructive and destructive. 
To form the first we take the whole conditional pro- 



CONDITIONAL SYLLOGISMS. 159 

'position as the major premiss ; the affirmation of the 

antecedent for the minor, from which premisses we 

shall draw the affirmation of the consequent as the 

conclusion; thus : 

Maj. prem. If A is B, C is D = If lie has a fever, he is sick. 
Min.prem. A is B = He has a fever. 

Conclusion. C is D = He is sick. 

To frame the destructive conditional syllogism, we 
take the whole proposition as before for a major pre- 
miss ; the denial of the consequent for a minor, and 
we deduce as a conclusion the denial of the antece- 
dent; thus : — 

Maj. prem. If A is B, C is D = If he has a fever, he is sick. 
Min. prem. C is not D. = He is not sick. 

Conclusion. A is not B = He has not a fever. 

As these are the only possible forms of conditional 
syllogisms, and as we have shown that all other forms 
of hypothetical propositions, disjunctive, causal, &c, 
may be easily reduced to conditional propositions ; we 
have only to show how these conditional syllogisms 
may be reduced to the form of simple categorical syl- 
logisms, and we shall, in effect, have shown it for all. 

Considering first, the constructive form, and remem- 
bering that the form of condition may be removed by 
the phrases "the case of," and "the present case;' 
and that the proposition assumes the form of a cate 
gorical proposition, of which the antecedent becomes 
the subject, and the consequent becomes a predicate, we 
shall have for the constructive form, 



160 



LOGIC. 



Maj. prem. The case of A being B 
Z 



Min. prem. 



Concl. 



or, 



The present case 
Z 


is 


r ^ 
The present case 

All X is Y. 
All Z is X. 
All Z is Y. 


is 

(A.) 
(A.) 
(A.) 



the 


case 


of C being D. 
X 


r 

the 


case 


of A being B. 
Y 



the case of C being D. 



which, X being the middle term, is evidently in the 
first figure, and the dictum may be at once applied. 
Using the same phraseology, and thus translating the 
destructive form, we have, 



x 



The< 


jase of A being 
Z 


B is 


r 

the case 


of C 
Y 


being D. 


The 


present 
Z 


case 


is not 
is not 


the case 


ofC 
X 


being D. 


t 

The 


present 


case 


the case 


of A 


■ \ 

being B. 






or, 


All X is Y 
No Z is Y. 
No Z is X. 


(A.) 
(E.) 
(E.) 







which, Y being the middle term, — is in the second 
figure, and in the mood Camestres, which must be re- 
duced to the first figure, or the form of the dictum. 

If, now, we perform the operations indicated to re- 
duce this mood (m, s, s), we simply convert the minor 



CONDITIONAL SYLLOGISMS. 161 

premiss, and then transpose the premisses, and simply 
convert the conclusion : we shall have, 

Y Z 



The case of C being D is not the present case. 
X Y 



The case of A being B is the case of being D. 
X Z 



The case of A being B is not the present case, 
or simply converting the conclusion, 

z x 



The present case is not the case of A being B. 

No Y is Z. (E.) 
AllXisY. (A.) 
NoXisZ. (E.) 



or, No Z is X. 
which is the form of Oelarent in the first figure. 

The logical form of the conditional does not depend 
upon the subject-matter of the propositions composing 
it. There may be, for example, two apparently inde- 
pendent propositions, that is, propositions in which 
the terms are entirely distinct, thus conjoined, or there 
may be a term the same in each ; which will cause no 
difference in the logical form : thus we may have 

If A is B, C is D = If John remain, James will go; or, 
If A is B, A is C = If the Bible is true, it (the Bible) deserves our 
attention. 

14* T, 



162 LOGIC. 

To explain this apparent difference, it will be re- 
membered that A, B, C, &c, although terms in the 
proposition, are not the terms of the syllogism when 
it is put in a categorical form ; but that the antece- 
dent and consequent become the true terms, and there- 
fore it matters not whether there be three or four 
independent terms in the conditional proposition 
before its change of form. # 

A few examples of conditional syllogisms are given 
to accustom the student to the form, and to guard 
him against the improper use of it. 

Examples. 
1. 
If the fourth commandment is obligatory upon us, we are bound 
to set apart one day in seven. 

But the fourth commandment is obligatory upon us. 
Therefore we are bound to set apart, &c. 

2. 

If any theory could be framed to explain the establishment of 
Christianity, by human causes, such a theory would have been 
proposed before now. 

But none has been proposed. 

Therefore, no such can be framed. 

3. 

If the eclipses of Jupiter's moons occur sixteen minutes later, 
when the earth is farthest from Jupiter than when she is nearest 
to Jupiter, light must travel ninety-five millions of miles in eight 
minutes. 

But these eclipses do occur so much later in the given position. 

Therefore light travels at the rate stated ; or, two hundred 

thousand miles in a second. 

4. 

If taste is uniform, all men will admire the same objects. 



DISJUNCTIVE SYLLOGISMS. 163 

But all men do not admire the same objects — (one sees beauty 
"where another only finds deformity). 
Therefore, taste is not uniform. 

Disjunctive Syllogisms. 

A disjunctive syllogism is one, the major premiss 
of which is a disjunctive propositio?i (26), and the 
minor a categorical. 

Brutus -was either a parricide or a patriot = Either A is B, or it is C. 
He was not a parricide = A is not B. 

He was a patriot = A is C. 

Here, when the major premiss consists of two 
members only, the minor asserts the one and the con- 
clusion denies the other ; or the minor denies the one 
and the conclusion asserts the other. Or we may 
have, instead of two alternatives, three or more; 
thus : — 

The angle A must be equal to, or greater or less than the angle B. 
But it is neither greater nor less than it. 
Therefore it is equal to it. 

It is evident that the disjunctive syllogism may be at 
once stated in a categorical form by any simple phrase- 
ology which will rid us of the disjunctive form ; thus : 

Brutus could not be at the same time a parricide and a patriot 
(but must be one of the two). 
He was a patriot. 
Therefore he was not a parricide, 
or, He was not a parricide, 
Therefore he was a patriot. 



164 LOGIC. 

Examples of Disjunctive Syllogisms. 

1. 

It is either true that knowledge is useful, or that ignorance is so. 
But it is not true that ignorance is useful. 
Therefore knowledge is so. 

2. 

Mahomet was either an enthusiast or an impostor. 

He was an enthusiast. 

Therefore he was not an impostor. 

This is Gibbon's argument, but it is faulty in point 
of fact, for a man may be both enthusiast and im- 
postor, — and some men have a great enthusiasm for 

imposture. 

3. 

A government either licenses a free press, or it is oppressive. 
The French government does not license a free press. 
Therefore it is oppressive. 

4. 
A wise lawgiver must either recognise future rewards and pun- 
ishments, or must appeal to an extraordinary Providence. 
Moses did not do the former. 
Therefore he must have done the latter. 

. Of the Dilemma, Trilemma, fie* 

A dilemma is a compound argument composed of 
conditional propositions, upon which we reason dis- 
junctively. When two conditional syllogisms are com- 
bined with a disjunctive minor premiss, the argument 
is called a dilemma. When three, four, &c, are so com- 
bined, they constitute a trilemma, tessaralemma, &c. 
The generic name Dilemma, however, is technically 
given to them all. Dilemmas are divided into four 

* 6tg ; rpsig, reaaapeg, &c, and \r]p.p.a, from Aa/i/Jayw, 



THE DILEMMA. 



165 



kinds, according to their being simple or complex, 
constructive or destructive. 

A simple dilemma is one in which we have as a 
major premiss, several antecedents, with a single con- 
sequent, thus: 



J If A is B, 
Maj. prem. -{ If C is D, then X is Y. Min. prem. 
If E is F, 



But either 
AisB 

or 
Cis D 

or 
E is F 



Conclusion. Therefore X is Y. 

A complex dilemma is one in which we have several 
antecedents, and each has its own consequent, thus : 

Either 



Maj. prem. - 



If A is B, G is H. 
If C is D, I is K. 
IfEisF, LisM. 



Conclusion. Therefore 



Min. prem. 



Either 
GisH 

or 
IisK 

or 
LisM 



AisB 

or 
Cis D 

or 
EisF 



Now, if in the simple dilemma, instead of reasoning 
as we have done constructively from the disjunctive 
affirmation of the antecedents to the disjunctive affirma- 
tion of the consequent, we reason destructively, that, 
is, deny the single consequent; then all the antecedents 
fall to the ground ; there is no longer the condition 
of the dilemma; for we have a simple conditional 



166 LOGIC. 

syllogism. Or if we have one antecedent and several 

consequents, and reason destructively, it is as though 

we had but one consequent, since the denial of any 

one requires the denial of the one antecedent ; thus, in 

the argument, 

f C is D, 

If A is B, G is H, 

[ L is M, 

it matters not whether we deny one or all the conse- 
quents, the denial of the antecedent follows. Hence, 
properly speaking, there is no such thing as a simple 
destructive dilemma. It differs in no wise from a 
simple destructive conditional syllogism. 

The destructive dilemma proper, then, consists of 
several antecedents, each with its own consequent, in 
which we disjunctively deny the consequents, that is, 
deny any one of them or all in turn, and we may 
disjunctively deny the antecedents. 

If A is B, CisD. „, But either C is not D, 

Maj.prem. T . Mm. prem. 

* r IfGisH, LisM. or Lis not M. 

&c. &c. 

Conclusion. Therefore either A is not B, 

or Gr is not H. 

To apply this abstract form to a particular example ; 
let us take the argument of Antisthenes : — 
_, . If we conduct the affairs of state well, we offend men. 

Jrlfl'). 7)TC7Tl» 

'If we conduct them ill, we offend the gods. 

If now we reason constructively we shall add, 

But, we must either conduct them well, 
Mm. prem. 

or conduct them ill. 

Conclusion. Therefore we must either offend men, 

or offend the gods. 



THE DILEMMA. 167 

If we reason destructively, we add — as a minor 
premiss, 

But we must either not offend men, or not offend the gods. 

and as a conclusion, 

Therefore, we must either not conduct them well, or not conduct 
them ill. 

To rid themselves of the perplexities of the dilemma, 
the old logicians always established from their pre- 
misses an undue, because not a logical conclusion, but 
a moral and material one, a passage of the mind to a 
purpose which had been suggested by the matter of 
the argument; thus, the conclusion of Antisthenes 
from the perplexity of the dilemma was, that we had 
better not meddle with the affairs of state at all. Take 
another illustration : — 

If a wife is beautiful, she excites jealousy ; 
If she is ugly, she gives disgust ; 

and the illogical, but common conclusion is, 
It is best not to marry. 

Most logicians have erred at the very outset, by 
supposing that, because there is an alternative ex- 
pressed in the dilemma, it is a disjunctive instead of 
a conditional syllogism, and thus have rendered it a 
vehicle of fallacy which it would be impossible foi 
Logic to arrest ; thus, they would read the last ex- 
ample, 

Either a wife excites jealousy by her beauty, 
Or disgust by her ugliness ; 
Hence it is better not to marry. 



168 LOGIC. 

In any such case$ if we first put the dilemma in its 
true conditional form, and then (leaving the province 
of Logic which presumes all given propositions to be 
true) examine the subject-matter of the propositions 
themselves, we shall find the falsity which causes per- 
plexity : thus, it is not true universally, nor commonly ', 
as is implied in the example, that if a wife is beauti- 
ful, she excites jealousy . It is even less true, that is 
in a fewer number of cases, that if she be ugly, she 
causes disgust ; hence the conclusion, that it is best 
not to marry is less true, i. e., applies to a fewer num- 
ber of cases than either of the foregoing assertions,- 
i. e. the falsehood is increased by the number of false 
statements preceding the conclusion. 

It is evident that the dilemma may be resolved into 
as many conditional syllogisms as the greatest num- 
ber of antecedents or consequents ; and that these 
may be reduced according to the rules for the reduc- 
tion of conditional syllogisms. 

Any dilemma may also be stated in a categorical 
form. Thus, 

The case of A being B, is the case of G being H. 
The case of C being D, is the case of E being F. 

and we may then proceed as in conditional syllogisms, 

Examples of the Dilemma. 

1. 

If Eschines joined in the public rejoicings, he was inconsistent. 

If he did not, he was unpatriotic. 

But either he did join, or he did not: — 

Therefore, he was either inconsistent, or unpatriotic. 



THE DILEMMA. 169 

The following dilemma was formed to confute the 
doctrine of Pyrrho, the sceptic, which was, that be- 
cause everything has its contradictory, everything is 
false; or, that no one could know anything cer- 
tainly. 

2. 

If what you say is true, then there is something which is not 
false (*. e. your system is wrong). 

If what you say is false, then it has no value as an argument (i. e. 
your system is wrong). 

But what you say must be either true or false. 

Therefore, in either case your system is wrong. 

There are two kinds of things which we ought not to fret about : 
what we can help, and what we cannot. 

(The student will put this in the form of a dilemma.) 

Having explained the various forms of argument, 
simple and compound, our next subject of investiga- 
tion is of the erroneous use of these forms ; to this 
has been given the generic title of Fallacies. 



15 



170 LOGIC. 



CHAPTER X. 



FALLACIES. 



(46.) The Meaning and Comprehension of a 
Fallacy* 

Different terms are used to express the errors 
which are found in terms, propositions, or arguments, 
in Logic. Thus, we say of a term, when it is not uni- 
vocal, i. e. when it has not one meaning, and only one, 
that it is equivocal or ambiguous, i. e. has more than one 
meaning ; of a proposition, if it be not true, that it is 
false, which expresses in other words, that the predi- 
cate and subject have no proper connexion ; of an 
argument we say, when it violates the dictum of Aris- 
totle or any of the rules given, that it is invalid, and 
sometimes of an invalid argument, we say that it is 
fallacious. 

A fallacy, then, is an invalid argument, which ap- 
pears at first sight to be valid. If it be used with the 
intention to deceive, the fallacy is called a sophism. An 

* Fallo — to deceive. 



FALLACIES. 171 

argument manifestly and foolishly invalid, would then 
be neither a sophism nor a fallacy. 

The subject of fallacies is one of the most import- 
ant in the study of Logic, for not only is Logic de- 
signed to teach us to reason correctly, but also it 
should teach us to perceive and detect all errors in 
reasoning ; hence we find the earliest writers on Logic 
giving rules and cautions for avoiding and detecting 
fallacies. 

The first division of fallacies which they have made 
is into fallacies in dictione, and extra dictionem. As 
dictio means the form of words and not the meaning 
of the words, or what is expressed in our word 
diction, the class in dictione, or fallacies in form, 
will evidently come within the province of Logic, 
while those extra dictionem, not being in the form, 
but in the subject-matter, with which Logic is only in- 
directly concerned, will really not fall within the 
scope of our study. 

But since the line between the two, although easy 
to be drawn, is continually mistaken in practical argu- 
ment or controversy unless it be thus drawn, it be- 
comes necessary to explain both classes with care, 
that we may always distinguish between the truly 
Logical and the non-Logical or material fallacies. 
One class of these material fallacies, which arises 
from the ambiguity in words, and is therefore called 



172 LOGIC. 

verbal fallacies, needs but a slight change, as we shall 
see, to become formal or logical fallacies. 

(47.) Of Fallacies in dictione, or Formal 
Fallacies. 

These are the fallacies, about which Logic is par- 
ticularly concerned. 

Under this class are included all violations of the 
dictum of Aristotle, and of the axioms and rules 
laid down for determining the validity of an argu- 
ment. The fallacy in all cases under this head is 
apparent in the form of the expression ; hence the 
name, formal fallacies. Of this kind are 

1. Undistributed middle terms. 

2. Illicit process of either term. 

3. Negative premisses. 

4. Affirmative conclusion from a negative premiss, 

and vice versa, 

5. More than three terms in the argument. 

Of these, repeated examples have been already 
given, in syllogistic form : it is only by putting them 
in this form that the fallacy is at once and easily 
detected. 

But it should be borne in mind that in practice, 
such fallacies are not stated in the syllogistic form, 
in which they are thus easily to be detected, but are 
stated in the form of an enthymeme, or other abridged 



FALLACIES. 173 

argument, and so covered with words that the effect 
is produced without the mind being convinced; the 
conclusion allowed, because the mind cannot see 
the false steps which have been used, although it has 
not certified itself that the true have been taken. 
Let the student then take the trouble, in each such 
case, to write out the argument in syllogistic form, 
and, for greater clearness, to use symbols, and the in- 
validity will be apparent. 

Thus, we are told that " a certain man was a good 
father, because he attended to the physical necessities 
of his children" ; food and clothing, and shelter, 
being the criterion of a good father. Let us apply 
the test of Logic to such an argument : — 
X Y 



,, . All good fathers provide for the physical wants of 

Maj.prem. & * . . * J 

their children. 

Z Y 



Mm. prem. A B did thus provide. 
Z X 



Therefore A B was a good father. 

Or, using symbols, 

All X is Y, 
Zis Y, 
ZisX. 

That is, — Y, which is the middle term, is undistributed, 
being the predicate in two affirmative premisses. 
Again, it is asserted that "brutes are not account 
15* 



174 LOGIC. 

able beings, because they are not responsible" ; 
"which involves a fallacy of illicit process. Thus, 
x j y . 



Maj. prem. All responsible beings are accountable. 
Z d X 



Min. prem. Brutes are not responsible beings. 
Z Y 



Therefore Brutes are not accountable. 

All X is Y, 
No Z is X, 
No Z is Y. 

In which Y, which is distributed in the conclusion, — 
being the predicate of a negative proposition, — is un- 
distributed in the major premiss : an illicit process of 
the major term. 

It will be observed in this latter instance, that the 
conclusion is, we believe, a true one, but it is not 
leached by such premisses ; and thus indeed it con- 
stantly happens, that men adopt a conclusion on inter- 
nal grounds which they cannot explain, and then seek 
in every direction for premisses by which to substan- 
tiate it : and so, on the other hand, many a just 
statement loses credence, from the fact that weak and 
empirical men undertake to prove it by false premisses 
or fallacious reasoning. 

It is further to be remarked, that men who are 
guilty of fallacy in argument, either through design 



MATERIAL FALLACIES. 175 

to deceive, or weakness of reasoning power, are apt 
to combine many single arguments into a compound 
argument. If, then, one of these be faulty in its 
ratiocination, every ulterior conclusion is endangered, 
and the whole chain of argument is fallacious. To 
detect the error, therefore, requires that the whole 
chain be exposed link by link, and that the proper 
tests be applied to each argument. We have given 
examples of the fallacy of undistributed middle, and 
illicit 'process ; the student will not need illustrations 
of the other formal fallacies mentioned. 

(48.) Material, or Informal Fallacies. 

It will be allowed that in every fallacious argument 
the conclusion does or does not follow from the 'pre- 
misses. If it do not follow from the premisses, then 
when written out by symbols the fallacy is apparent, 
coming under one of the heads of formal fallacies 
which we have just enumerated. The fault here is 
evidently in the reasoning ; but when the conclusion 
does follow from the premisses ; when, written out by 
symbols, the fallacy is not apparent, the fault will 
not lie in the reasoning, but either in the premisses or 
in the conclusion, i. e. as to their truth or falsity, or 
as to the ambiguous meaning of words used in both. 
Such fallacies, with which Logic is not directly con- 
cerned, are called Material Fallacies. 

It has been remarked before, that Logic indeed 



176 LOGIC. 

takes for granted that the propositions composing its 
syllogisms are true ; and that when we write the 
general proposition A is B, no meanings shall be 
given to A and B which shall violate the truth of the 
proposition. If then we put for A, Learning, and 
for B, useless, and thus write, 

Learning is useless, 

or, by a change of words, the doctrine of the Stoics, 

Pain is (a lesser sort of) pleasure, 

we shall reason to false conclusions, the matter of 
the propositions forming the syllogism being false, 
while the logic of the argument may be correct. It must 
be allowed that material fallacies are more numerous, 
and more fruitful causes of error, than the logical, and 
as such deserve a special consideration, although in- 
directly allied to our subject. 

We shall, therefore, endeavour briefly to give the 
principal forms or titles of material fallacies, and to 
illustrate them by examples, observing at the outset, 
that they assume many and varied forms under these 
titles, all of which we cannot take the time to consider. 

The simplest division of them is one which grows 
out of the consideration of 

1. Errors in the premisses. 

2. Errors in the conclusion. 

Of Errors in the Premisses. 
Logicians have adopted technical names for the 



MATERIAL FALLACIES. 177 

fallacies of this kind ; viz. : — the petitio principii, or 
begging the question ; Arguing in a circle ; Non causa 
pro causa, or the assignment of a false or undue 
cause. These branch out into various minor divisions. 
As all these grow out of a false or undue assump- 
tion of premisses, they are akin to each other, and 
in many cases are not easily to be distinguished. 
Especially is this true of the first two. 

I. Petitio principii. This consists in using as a 
premiss to support an adopted conclusion or assertion, 
the same fact in other words. Thus we are told that 
" if the heart be touched death ensues, because it is 
a vital part," or that « morphia produces sleep because 
it is an anodyne." 

Now what is it to say, but that death ensues, when 
the heart is touched, because death does ensue; or 
that morphia produces sleep, because it produces sleep. 

Our language, which has so many synonyms from 
the Anglo-Saxon and the Latin, gives full play to 
this sort of fallacy, and many a wordy man is guilty 
of it without knowing his own error. And besides, 
this fallacy is the just recompense of those who en- 
deavour to prove axioms, or who seek to penetrate into 
the ultimate facts for which God assigns no cause but 
the fiat of his own will. 

II. Arguing in a circle. This fallacy depends 

upon finding a premiss to prove an asserted conclusion, 

and then, when asked for the proof of the truth of 

M 



178 LOGIC. 

that premiss, endeavoring to make the conclusion 
prove the premiss ; or, as this would be easy of de- 
tection, to make the circle still larger, i. e., proving 
the truth of the premiss by a third proposition which 
depends upon the conclusion, and then playing upon 
these three, like the juggler's balls of which one is 
always in the air, but which — it is very difficult 
to tell. In case of the simplest form, writing out 
the syllogism will detect it ; and in the latter and 
more complex case, the sorites, or its syllogisms 
written out, will find it out. 

Thus ; many men, not content with the everywhere 
shiniDg proof within and without that there is a God, 
and mistaking the relations which the Holy Scrip- 
tures bear to him, would prove the existence of a 
God from the truth of the Scriptures, and then prove 
the inspiration of the Scriptures from the fact that 
they came from Q-od. 

As the Scriptures are the word of God, what they declare must be true. 
The Scripture* declare that God exists. 
Therefore That God exists is true. 

Or again ; 

The word of God must be true. 
The Scriptures are the word of God. 
The Scriptures are true. 

III. Non Causa pro causa. This fallacy, which 
indeed may stand for the general title of unduly as- 
sumed premisses, consists technically in assigning as a 
reason or cause in the premisses, one which has nothing 



MATERIAL FALLACIES. 179 

to do with the conclusion, or one which is not itself 
proven, and is not therefore a sufficient cause. The 
first of these errors is called the fallacy of a non tali 
causa pro tali, or the assignment of a cause as though 
it were a cause, when it is not ; and the second is the 
a non vera jiro vera, in which the assumed premiss 
cannot be proven to be true as a cause, and may 
therefore be considered false. 

Of the latter of these, the a non vera, we find a 
striking example, and an excellent logical retort, in 
the reported dialogue between Charles II. and Milton, 
after the poet had become blind. " Think you not," 
said the king, " that the crime which you committed 
against my father must have been very great, seeing 
that Heaven has seen fit to punish it by such a severe 
loss as that which you have sustained ?" " Nay, sire," 
Milton replied, "if my crime on that account be ad- 
judged great, how much greater must have been the 
criminality of your father, seeing that I have only 
lost my eyes, but he his head." Another and com- 
mon example of this is the following: — 

The natives of barbarous countries regard an eclipse 
as portentous of war and famine, and should they come 
together, they would assign it as the cause of their 
trouble. We know that it is not ; but they only note 
to the conjunction of the two as satisfactory proof that 
it is. Either of these may be easily written out in 
the syllogistic form, in which the propositions can be 



180 LOGIC. 

scrutinized as to their subject-matter, and the falsity- 
detected. Of the a non tali, the following example 
will serve as an illustration ; viz. : — 

All poisons should be avoided. 
Brandy and wine are poisons. 
Therefore They should be avoided. 

That is, they are poisons only when taken in certain 

amounts and under certain circumstances. This is an 

invalid argument used by many good persons. The 

true reason for avoiding brandy and wine being the 

danger of acquiring a habit of using them to such an 

extent that they will be poisons. 

Errors in the Conclusion. 

"We come now to the second division of material 
fallacies, those in which the error lies in the conclusion; 
they are all included under the general head of Igno- 
ratio elenchi, or irrelevant conclusion. 

The word elenchus, as used in the early writers, 
meant the contradictory of your opponent's assertion, 
and thus implies, what indeed was a feature in earlier 
Logic, the existence of an opponent. Dialectics were 
almost always in the form of dialogue, and the 
Socratic mode of questions and answers was adopted 
as the acutest method of argument. 

The disputatious spirit of the Greeks was as much 
concerned about the victory in logomachy or tvord- 
war, as about the discovery of truth, and hence arose 
many of their errors and paradoxes. This spirit of 



MATERIAL FALLACIES. 181 

controversy, and the constant keeping in sight of the 
elenchus has pervaded the methods of Logic to a very 
late period. 

The ignoratio elenchi is the ignorance of the contra- 
dictory of our opponent's assertion, which we display 
when, instead of establishing the elenchus, i. e. proving 
the contradictory, and thus proving his conclusion or 
assertion false, we attempt to establish something re- 
sembling the contradictory. 

As it is not our purpose to reproduce the Grecian 
technicalities and method, let us get rid of this name 
and form, and call the fallacy, as it has been called 
by modern writers, the fallacy of irrelevant con- 
clusion. 

Those who employ it, and this, it may be remarked, 
is the most common and practical of all the material 
fallacies, generally state the conclusion as a fact, and 
when asked for the premisses or proof, are compelled 
to present such as display the irrelevancy of the con- 
clusion. Thus, one asserts the fact that « Alfred the 
great was a scholar," and when asked for proof, says, 
"because he founded the University of Oxford.''' 
Now, there may be distinct proofs that he was a 
scholar, but this certainly is not conclusive. Let us 
state the syllogism : — 

Those who found universities are patrons of learning ; 
Alfred the great founded the University of Oxford ; 
Therefore, he was a scholar. , 

16 



182 LOGIC. 

The conclusion is irrelevant ; the true conclusion 
being, from these premisses, that 

He was a patron of learning. 

If polemical writings, and especially those which 
partake of the nature of popular and heated contro- 
versy, be analyzed, this will be found to be the stand- 
ing fallacy, as often self-deceiving as deceiving others, 
and responsible for much of the wide-spread error in 
speculative science. 

So varied is its nature, that it has been from the 
early times known under various names, and presents 
its insidious temptations to all kinds of persons. 

Perhaps that form which is of most universal appli- 
cation is the argumentum ad Jwminem, the unfair 
appeal to personal opinions, or to ones vanity or pre- 
judice. After exhausting all the arts to prove a 
thing wrong which is not so, the argument closes with 
"Well, you would not do so !" Even in matters of 
religion we are triumphed over by the adversary by 
a reference to ourselves and our own imperfect 
actions, when the question concerns the abstract 
truths of God's holy law. This form of the fallacy 
needs, then, a special watch as the most insidious. 

Next in enumeration is the argumentum ad popu- 
lum, which is the former fallacy extended from one 
individual to many, from personal opinion to popular 
prejudice 



MATERIAL FALLACIES. 183 

Unprincipled demagogues use this fallacy con- 
tinually ; and where the sophistry would be apparent 
to any single mind gifted with common sense, the 
enthusiasm and thoughtless spirit of a mob, moved 
by a fiery harangue, is blind to its unreasonableness. 
This may be called the logic of revolutions. 

A third kind of irrelevant conclusion is the argu- 
mentum ad verecundiam, or appeal to the modesty of 
our opponent, hoping that he will not presume to 
attack respected authorities and time-honoured cus- 
toms. Although healthful progress may have de- 
monstrated their errors, and provided us with better 
methods, the cry is of recreancy to our fathers' memo- 
ries, to old associations, to History ; and thus the 
world has been trammelled and clogged by what pro- 
fesses to be the genius of conservatism, but what is 
in reality the genius of obstinate error. 

Besides these forms of irrelevant conclusion, there 
are many which have been proposed in pleasantry, 
such as the argumentum ad baculinum, and others 
which Sterne humorously refers to in « Tristram 
Shandy." 

There are, however, it must be particularly observed, 
many cases in which these very arguments are not fal- 
lacies ; in which, indeed, they may with great propriety 
be used, clothed with all the graces of rhetoric and 
imbued with all the fire of enthusiasm. 

The argumentum ad hominem is not a fallacy when 



184 LOGIC. 

the design is to teach pure truth, and when no unholy 
passion or emotion of man is appealed to. In this 
application it was used by our Saviour himself to the 
Jews on many occasions, with great force and beauty. 
His touching, and yet searching, appeal to them for 
^ the woman taken in adultery, sent them out one by 
one before its power. Each one felt the argument 
and admitted the conclusion. 

His arguments in favour of healing on the Sabbath, 
and searching the Scriptures, that they might find 
every page luminous with Him whom they denied, 
were examples of the unfallacious and powerful use 
of this form of reasoning. 

So, too, an appeal (ad populum), not to the preju- 
dices, but to the conscientious scruples and feelings of 
a multitude, is without fallacy, and is productive of 
the best results. 

Many customs, long honoured, and dear to every 
heart ; customs national, civic, professional, domestic, 
unmingled with error, unopposed to progress, make 
the argumentum ad verecundiam a most proper and 
effective appeal. 

But such is the waywardness of man that the temp- 
tation to fallacy in their use is exceedingly strong, 
and must be carefully guarded. 

Argumentum ad rem and ad judicium. 
Opposed to all these, when used as fallacies, are two 
forms of valid argument : the first expresses a cod 

to Lwi , -~ 

-, 



FALLACY OF OBJECTIONS. 185 

centration solely upon the reason of the thing itself, 
and is therefore called the argumentum ad rem ; the 
second is when the appeal is made to the unbiassed 
exercise of the individual judgment: this argument 
is called argumentum ad judicium. Many writers 
have increased the number of these fallacious argu- 
menta to a much greater extent; but those given are 
the principal ones, and will sufficiently indicate the 
process by which they are coined when needed. 

Changing the 'point in dispute. 
Another form of the "irrelevant conclusion" is the 
fallacy of changing the point in dispute, in which one 
of the parties in a long and difficult controversy, after 
having tried in vain to establish his irrelevant conclu- 
sion, dexterously shifts his ground from the point in 
dispute to some other, and pertinaciously claims that 
to be true which has not been disputed, while the true 
matter of contention is left, without an honest confes- 
sion of his inability to prove his assertion. For ex- 
ample, a person undertakes to prove that the people in 
general are not educated ; •'. e., he first denies that they 
are ; but failing of this, he really proves, what no one 
denies, viz. : that all the people should be educated. 

Fallacy of Objections. 

It has been remarked, that Ignorance may state in 

a few words objections against Science, which wise men 

could not refute in whole volumes. The truth of this 
16* 



186 LOGIC. 

is manifest. The error of reasoning from the state- 
ment or existence of these objections, to the falsity 
of the science, is one of the forms of irrelevant con- 
clusion which has been called the Fallacy of Objec- 
tions. It consists in asserting that, since there are 
objections against a Science, that Science is false; 
whereas the judgment demands that the claims of the 
Science as well as the objections be duly stated : and 
that the turning of the scale decide whether truth or 
error predominate. If it be a complicated system, it 
will be found to contain portions of both ; if an ab- 
stract theory, it will stand or fall by such a test. 
This fallacy has been industriously aimed by scep- 
tics against the mysteries of the Christian faith, but 
it soon loses its point in such an encounter. 

From the consideration of the various species of 
the fallacy of irrelevant conclusion which have been 
mentioned, and the examples given, it will be seen 
that it is in all its forms the standing sophism in houses 
of legislative convocation ; that it is the demon of de- 
bate. Few subjects of debate are so abstract and unit- 
like but that dull minds will find room to wander about, 
one losing the very point in question, another con- 
cerned about a crowd of details which have little or 
no bearing upon it, a third mistaking the fine and 
delicate points of the logical argument ; some, becom- 
ing heated in the controversy, will lose their temper 
and reasoning powers together, and overpowered by 



MATERIAL FALLACIES. 1ST 

the truth and Logic of their opponents, will have re- 
course to appeals to the prejudices and interests of 
their audience ; and others, more shrewd than just, will 
seek to hring by similar means the cause and persons 
of their adversaries into disrepute, by the light arrows 
of ridicule, or the more ponderous weapons of insult. 
It is amidst such scenes, and under such circumstan- 
ces, that the master mind shows itself as it rises over 
the storm of the debate, and brings them back first 
to the consideration of the subject in dispute, in its 
true and abstract form. Perhaps the most striking 
illustration of this is found in our own Congressional 
history. After Mr. Webster's first speech on " Foote's <?/ 
resolution," many senators had delivered their views, 
and much sectional excitement was aroused. Mr. 
Webster began his famous second speech, with just 
such a master-effort to come back to the true merits 
of the controversy : — 

"Mr. President, — When the mariner has been tossed for many 
days in thick weather and on an unknown sea, he naturally avails 
himself of the first pause in the storm, the earliest glance of the 
sun, to take his latitude, and ascertain how far the elements have 
driven him from his true course. Let us imitate this prudence, and 
before we float farther on the waves of this debate, refer to the 
point from which we departed, that we may at least be able to con- 
jecture where we now are. I ask for the reading of the resolution 
before the Senate." 

The resolution was read ; the Senate found their 
true position, and Mr. Webster's speech is as mas- 
terly for its logic as for its oratory. 



188 LOGIC. 

(49.) Verbal Fallacies. 

There is still a most important class of invalid 
arguments to be considered ; it is that growing out 
of the ambiguous or equivocal meanings of words ; 
many words being identically the same, and yet bear- 
ing widely different meanings. Thus, the simple word 
line, when used in different connexions, means many 
distinct things ; for example : — a cord used in fishing ; 
a few words in a letter ; an arrangement of troops or 
ships in battle array ; and when we see the word 
porter, we are in doubt which of three meanings is 
intended, — a gate or door-keeper, a man who bears 
burdens, or a hind of malt drink. 

In most such cases, however, there is a single root 
to which we may trace all these secondary meanings ; 
thus all the meanings of a line refer to the mathema- 
tical definition that it is length, without breadth or 
thickness, and all the uses of porter refer to the Latin 
word which signifies to bear. 

It is true that there are examples of words spelt 
alike which have different etymologies ; but these are 
few : host, from hostis, and host from hqstia^ in the 
sacrifice of the mass, are examples of this ; so also 
league from ligare to bind, and league from the Latin 
locus or distance between places, contracted in French 
to lieue, as the word focus is into feu ; — are examples 
of such words. With these few illustrations of am- 



(/Wv^_ 



'YW/vW^, 



* 5) 



VERBAL FALLACIES. 189 

biguous terms, let us see how they are used in argu- 
ment. 

The ambiguous word is sometimes the middle term, 
and sometimes it is the major or minor ; in most cases, 
however, it assumes the former place, so that the 
general name given to this form of verbal fallacy, is 
" the Ambiguous middle." 

X Y 



The church is the company of faithful people. 
Z X 



This stone building is the church. 
Therefore This stone building is the company, &c. 

Now, if this glaring and absurd fallacy be stated 
by symbols, we shall have 

X is Y, 
ZisX, 
Z is Y, 

which is the form of a valid argument in the first 
figure ; so that the fault lies in the matter of the 
propositions which compose the argument, and not in 
the form, which is correct ; the fallacy then must be 
classed, with such an investigation, among the mate- 
rial, and not among the formal fallacies. But let us 
go a step farther; since "the church" in the major 
premiss means something entirely different from "the 
church" in the minor, they are in reality different 
terms ; let us symbolize them by different letters, and 



190 LOGIC. 

calling the first X, let us call the second P ; we shall 
have, writing by symbols, as before, 

Xis Y, 
Zis P, 
ZisY, 

a formal fallacy, in which there are, contrary to the 
rules laid down, four terms instead of threes and 
this comes within the province of Logic. The fallacy 
of Ambiguous middle has very justly, then, been called 
by logicians, a semi-logical fallacy ; before we dis- 
cern the ambiguity it is a material fallacy, with which 
Logic is not concerned ; but as soon as we discover 
the ambiguity, it discloses four terms, which make it a 
formal or logical fallacy . It is because of this pecu- 
liarity, and because it is so very much used in com- 
mon life, that we treat of it under the distinct head 
of verbal fallacies. But we have said that it is not 
only in the middle term that this ambiguity occurs ; 
it also happens in the major and minor terms ; and is 
quite as sophistic when it lurks there as in the middle 
term. We have therefore discarded the title " Ambi- 
guous middle," as applied to the general class, pre- 
ferring "Verbal fallacies," as more truly illustrative 
of the error in any of the terms. 

There are many ways in which words are used 
ambiguously, and we shall give a few of them with 
illustrations ; and first, we place the influence of 
Etymology. 



ETYMOLOGY. 191 

I. Etymology, 

A word which originally meant one thing, now means 
quite another, and the fallacy consists in using it in 
the two senses, in two propositions of the syllogism. 
Thus, taking the first meaning of pagan to be a villa- 
ger (paganus*), and its present meaning to be a be- 
liever in some other religion than that of Christ, we 
have, 

& pagan is a disbeliever in Christ; 

Every villager is a pagan ; 

Every villager is a disbeliever in Christ. 

Akin to this, and indeed ranging under the general 
subject of etymology, is the use of paronyms, or pa- 
ronymous words. 

Paronymous words, are the noun substantive, ad- 
jective, verb, &c, belonging to each other and spring- 
ing from the same root. To project, prdject, pro- 
jection, projector, &c, are paronyms, springing from 
the Latin compound of pro and jaceo. So presume 
(in its two senses), presumption, presumptive, pre- 
sumptuous, &c, are paronyms growing from the root 
presumo. 

Take the following example, in which the ambi- 
guity will lie in the middle term : — 

Presumption is impertinence ; 

That the sun shines, I presume (or, is my presumption) ; 

Therefore I am impertinent (in asserting that the sun shines). 

* From pagus, a village. 



192 LOGIC. 

It will be remembered that the true logical form of 
the minor premiss, which is usually written, "I pre- 
sume that the sun shines," is 

subj. pred. 



That the sua shines is presumed by me. 

Again : 

To propose a railroad is a project (or a projector' 's work.) 
This man proposed a railroad. 
Therefore He is a, projector. 

in which the ambiguity lies in the major term. Now, 
no one can work advisedly, without making projects, 
whereas one of the meanings of projector, is a schem- 
ing and visionary man, who ought not to be relied 
upon. 

II. Fallacy of Interrogations. 

This is a use of two or more terms in a question, 
making thus in reality two questions, requiring two 
distinct answers, and the ambiguity lies in the single 
answer given to both. It is common for those who 
use this fallacy to express but one question, while the 
other is implied. Thus, if a man who has always 
been temperate is asked, « when he gave up drinking ?" 
the implied question is, "did he ever drink?" and 
then, if so, when did he cease ? or, in the celebrated 
inquiry of King Charles II., " why a dead fish does 
not add to the weight of a vessel of water?" the im- 
plied question being " does a dead fish add, &c. ?" and 



FALLACY OF INTERROGATIONS. 198 

if so, "why, &c." This fallacy, which is called by 
the writers, Fallacia plurimum interrogationum, is 
made more subtle by the number, and closeness of 
resemblance, of the points included in the questions. 

III. Amphibolous Sentences. 

Sometimes the ambiguity, instead of residing in the 
words which compose the argument, lies in the con- 
struction, and thus, by different punctuations, we 
have double and opposite meanings. This passes 
from the ambiguous words to amphibolous sentences. 
Among the most celebrated of these is the response 
of the Delphic oracle to Pyrrhus when he went to 
encounter the Romans : — 

Aio te JEacida Romanos vincere posse, 
Ibis redibis nunquam in bello peribis. 

In the first line, either accusative may be taken 
with the infinitive, thus making either « Pyrrhus," or 
"the Romans," able to conquer ; and in the second, 
nunquam may qualify either redibis or peribis. 

So also in the Nicene Creed, we have, in reference 
to our Saviour, the words — "being of one substance 
with the Father, by whom all things were made." 

The latter clause, so manifestly introduced by the 

Council, to declare the creative power and Godhead 

of Christ, in reality by strict rhetoric applies to 

"the Father." 

The name given to this fallacy is the fallacy of 
17 N 



194 LOGIC. 

amphibolous * sentences, i. e., tossed from one to 
another, with a doubtful meaning. 

Causes of Ambiguity. 

Having mentioned the various kinds of ambiguity 
in words, we come to consider why words have two or 
more meanings. 

We have already seen that many words expressing 
simple primitive ideas grow by usage to have other 
meanings, in which, however, the primitive idea is to 
some extent retained : thus, line, in all its meanings, 
adheres to the mathematical notion of extension in 
length. 

Now, without being able to trace the exact process 
in all cases, by which a word is thus gradually changed, 
we find that it ranges itself under one of these heads : 
1. Resemblance; 2. Analogy; 3. Association ; 4. El- 
lipsis ; 5. Accident. 

1. Resemblance. Many things bear the same name, 
from their actual similarity in appearance. Thus, in 
carpentry, a dove-tailed joint is so called from its 
similarity to a dove's tail, or a spear of grass from 
its resemblance to the military weapon, a spear. So 
in the military art, a "priest-cap," or " swallow-tail" 
is a redoubt so named from its actual resemblance to 
these two things, and a « crow's foot" takes its name 
from the form of a bird's talons. 

* a[i(pi and /?aAXa>. 



ASSOCIATION. 195 

2. Analogy. Our ordinary speech is full of the use 
of this figure of speech, and this fact has contributed 
to the ambiguity in many words. As resemblance is 
a similarity in appearance, analogy is a similarity in 
use, purpose, or relation. Thus, we speak of the arm 
of a chair, because it holds the relation to the chair 
which the arm does to the human body : and thus an 
arm-chair is a chair which has arms. 

We speak equally of a sweet food, or a sweet sound, 
because there is a similarity between the relations of 
the food to the palate, and the sound to the ear. So 
a sour lemon and a sour individual, create relatively 
similar effects upon the taste and upon the mind. 

Ambiguity of resemblance and of analogy are both 
produced and perpetuated by the use of metaphor 
and comparison, in our ordinary discourse, and a way- 
ward fancy, expressing itself in the social exaggera- 
tions of the day, is robbing some of our best words 
of their true shades of meaning : for example, sweet, 
lovely, horrid, agony, wretch, are deflected from their 
original meanings entirely. 

3. Association. By this we mean the connexion 
of parts in the same structure or institution, or to pro- 
duce a single result. Thus, a door is the opening in 
the wall, or the swinging shutter that closes it. Faith 
is belief, and "the Faith" is the system of Christi- 
anity. Shot is the leaden pellet : a good shot is 
either the person who shoots, or the effect of the shot. 



196 LOGIC. 

It is by the association of ideas, which, unlike our 
examples, are subtle and difficult to fix and determine, 
that fallacies have grown out of this ambiguity; and 
such is the want of correctness in the language of 
the great number of people, that the tendency to this 
fallacy of words, expressing associated ideas, is par- 
ticularly strong and dangerous. 

4. Ellipsis. Another habit into which men natu- 
rally fall, in trying to avoid the use of many words, 
and words conveying thoughts which the mind will 
readily supply without their being expressed, is the 
use of elliptical language. While in most cases this 
is harmless and even profitable, in some it leads to 
error. Thus, we speak constantly of Scott, Byron, 
&c, when we mean their works or their persons. We 
use the form " to my father's," " at Mrs. Smith's," when 
we mean the houses or " parties" of these persons, and 
such ellipsis is always understood ; but many persons 
are deceived in their business relations by such 
ellipsis as the statement of another's wealth at so 
many thousands of dollars, when in reality, although 
it may produce the interest on such a sum, it cannot 
be made available for anything like the amount of 
the principal sum mentioned. 

5. Accident. It seems in certain cases as though a 
word had assumed two meanings in a manner inex- 
plicable and accidental. Such, for example, is the 
word light, which is equally opposed to heavy and 



ACCIDENT. 197 

dark : and which in conduct means the opposite of 
serious or dignified. But even in such a case we 
shall find one idea, however subtle, pervading them 
all, and that is the removal of a covering of some 
sort ; thus, light removes the pall or covering of 
darkness ; the incumbent weight of something heavy ; 
the just restraints of dignity and sobriety. In strict 
truth, then, there is no accidental ambiguity, for, 
although there may be words in the double meanings 
of which we can discover no relation to a single idea, 
that relation undoubtedly exists, and by a profound 
research the number of such words would be very 
much diminished. 

Many words are forced into a double meaning by 
a popular or political use, which may be called acci- 
dental, but which in reality is designed by one party 
as an equivoque, or -stratagem, in the way of retort 
upon the other. It was thus with the use made of the 
word Pretender, by the English Jacobites. When it 
became treasonable in any way to maintain the claims 
of James Stuart, the son of James II., who was called 
"the Pretender," they toasted him in the well-known 
verses : — 

God bless the king; God bless the Faith's Defender; 
God bless — no harm in blessing — the Pretender. 
But -which is the Pretender ; which the king ? 
God bless us all, — that's quite a different thing. 

It is evident that such a use of the word would de- 
ceive no one ; nor was it indeed so designed, but rather 
17 * 



198 LOGIC. 

to violate the spirit and yet adhere to the letter of 

the law. The true argument used by the adherents 

of the new dynasty, was — 

Those who aid a pretender to the English throne, deserve pun- 
ishment. 

James Stuart is a pretender. 

Those who aid James Stuart, deserve punishment. 

It must be understood that pretender in both pre- 
misses has the same meaning, i. e., false claimant. 

But there is still another form of ambiguity which 
leads to fallacious arguments ; it is where the ambi- 
guity lies not in words but in the context; or where 
our assertion means one thing when taken in a general 
sense, and quite another if considered in a special 
sense. Of these fallacies, arising from ambiguity in 
the context, there are two kinds. 

1. The fallacy of accidents. 

2. The fallacy of division and composition. 
Under the first head are included the Fallacia acci- 

dentis, and the Fallacia a dicto secundum quid ad 

dictum simpliciter. These are the converse of each 

other. 

Fallacia accidentis. 

This is where, in one premiss, we assert something 
of a subject in a general sense, and, in the other, place 
upon that subject some accidental peculiarity, which 
will lead us to error in the conclusion ; thus, 

Things bought in market we eat. 
Raw meat is a thing bought in market. 
Therefore, Raw meat is what we eat. 



FALLACY OF DIVISION AND COMPOSITION. 199 

Here the middle term is things bought in market, and 
it is considered in the major premiss as to its essence ; 
viz. : that these things are in market for general use as 
food ; in the minor we lose sight of its essence, and only 
regard some accident of it, viz. : that the meat bought 
in market is raw. Thus, in reality, the error is thrown 
upon the middle term, which is shown to be not one, 
but two distinct terms, and the fallacy is thus exposed. 
The other form of this, which for shortness is 
called the Fallacy of Quid, may be translated reason- 
ing from the restricted or limited sense of a term 
(secundum quid — i. e. aliquicl in the monkish Latin), 
to its broad or unrestricted use (ad dictum simpliciter). 
Thus :— 

This man is innocent (of a certain crime), 
But the innocent (entirely) are sure of Heaven ; 
Therefore This man is sure of Heaven. 

Fallacy of Division and Composition. 
In this fallacy the middle term is used in its collec- 
tive or additive sense in one premiss, and in its dis- 
tributive sense in the other. When the middle term 
is used collectively in the major premiss, and distri- 
butive^ in the minor, the fallacy is of " Division" • 
when the reverse takes place, it is a fallacy of 
" Composition." The following are examples : — 

Fallacy of Division. 
The Christians (as a sect) were persecuted at Rome. 
Constantine was a Christian (individually), 
Therefore He was persecuted at Rome. 



200 LOGIC. 

Fallacy of Composition. 

Three and two are two numbers (distributively). 
Five is three and two (additively). 
Five is two numbers. 

Positive and Negative Intention. 

Akin to these fallacies are those absurd conclusions 
reached by a play upon certain negative words, such 
as nothing, and no, when used as an adjective; thus: 

Nothing is better than Heaven. 
A shilling is better than nothing. 
Therefore A shilling is better than Heaven. 

No cat has two tails. 

Every cat has one tail more than no cat. 

Every cat has three tails. 

In these examples the middle terms nothing and 
no cat, are taken in a positive sense in the major 
premiss, as though they expressed living or existing 
things, while in reality they mean non-existence. In 
the minor premiss they are taken in their true nega- 
tive sense. 

The best method of refuting them is to deny the 
major premiss, or to demand that it be put in other 
words, thus : — 

It is not true of anything that it is better than Heaven : 

which will foil the one who wishes to draw the absurd 
conclusion. It should be observed that such argu- 
ments are really used only in sport, but it is well to 
detect and understand the error which they contain. 



^ 



REMOVING AMBIGUITY IN TERMS. 201 

(50.) The Manner of removing Ambiguity in 
Terms. 

The true method of ridding ourselves of this ambi- 
guity of terms in argument, is to demand a defini- 
tion, in each case, and to keep owe. terms distinct when 
thus defined. It will not, in most cases, be neces- 
sary to give a real definition, as a nominal one will 
answer every purpose. The ambiguity is usually 
such that by giving the true, limited and exact name 
(which is the province of a nominal definition), we 
shall detect and remove it. 

In many cases where the fallacies consist of a num- 
ber of arguments and many ambiguous terms, the 
first thing to be done is to disentangle the web of 
sophistry, by writing them out in full, and in due 
order, and then after detecting the terms in which the 
ambiguity lies, to demand a definition in a few but 
plain and conclusive words, in every case. 

The equivocal nature of the word becomes appa- 
rent, if we change the language, as in the translation 
of the familiar example, into Latin : — 

Light is contrary to darkness. 
Feathers are light. 
Therefore, Feathers are contrary to darkness. 

we shall have, 

Lux est contraria tenehris, 

PlumEe sunt leves. 

Plumae sunt contrarise tenebris.* 

* Latham's Logic, p. 221. 



202 LOGIC. 

This change of language, it will be seen, is of the 
nature of a definition. 

(51.) The Fallacy of Probabilities, or the Calcu- 
lation of Chances. 

This consists in stating two probable premisses, and 
then drawing a certain conclusion, as though the 
number of probabilities combined amount to cer- 
tainty, whereas, in most cases, the conclusion will be 
less probable than either ; thus : — 

Those who have the plague probably die ; 
This man probably has the plague ; 
Therefore He will [certainly) die. 

Whereas, suppose ten out of twelve of those who 
have the plague die, then, if we express certainty by 
the number 1, that probability is expressed by the 
fraction \% or §, and if it is an even chance whether 
or not he has the plague, that probability will be ex- 
pressed by J. The probability of the conclusion, 
therefore, will be § X J = j%, or as J- is the expression 
for perfect doubt, i. e., an even chance of his living 
or dying, he is less likely to die than to live, his chances 
of dying being 5 out of 12, and of living, 7 out of 12. 

This fallacy is practically used in times of sickness 
and mortality, when fear of evil, excited by nervous- 
ness, affection, &c, place an anticipated conclusion 
for the true one. 

When instead of one syllogism, or enthymeme. 



FALLACY OF PROBABILITIES. 203 

many are combined to make a compound argument, 
and the errors of probability are thus multiplied, the 
result will be at once farther from the truth, and 
more difficult to detect. 

Let us deduce then a simple rule for the calculation 
of probabilities. The subject has been called « the 
doctrine of chances." 

When we speak of chance* we really mean probable 
results of GrocVs laws, and in the use of either word, 
we express our ignorance of the connexion between 
natural causes and effects. Now, as that ignorance 
may be partial or entire, the probability ranges be- 
tween the two extremes, certainty and impossibility. 
We do not pretend to assert by this that man may divine 
the results of God's doings in the future ; but that 
according to the action of natural laws, and the se- 
quence of an established order, we may approximate 
to the truth without assuring ourselves of it. 

Thus, in throwing dice, we cannot be sure that any 
single face or combination of faces will appear ; but 
if, in very many throws, some particular face has not 
appeared, the chances of its coming up are stronger 
and stronger, until they approach very near to cer- 
tainty. It must come ; and as each throw is made 
and it fails to appear, the certainty of its coming 
draws nearer and nearer. 

The probability of a single event depends upon the 
number of chances, of which it is one ; thus, if A. is 



204 LOGIC. 

in a single action where 10 men are killed, his com- 
pany numbering 50, the chance which each man 
stands of being killed, and consequently that of A, 
is Jg or J. If we subtract \ from 1, or certainty, we 
shall have % for his chance of being saved. The cal- 
culation of probabilities becomes more complicated 
where the events are combined. Thus, if in a second 
action 10 men more are killed, his chance of being 
killed in this last action, is as 10 to 40, or J : and that 
of his being saved f . If now we would determine his 
chance of being saved, after both actions, we must mul- 
tiply the two chances together : | X f = 28 = f , 
which is as it should be, since 20 men are lost of the 
original 50, and 30 remain, his chance of being among 
the latter should be as 30 to 50, or |. 

It is upon this principle of calculating chances that 
insurance companies are founded ; and it finds a bene- 
volent issue and scope particularly in those Life-assu- 
rance companies, which, demanding but a small per- 
centage, making a large aggregate, are thus enabled 
to pay to widows and orphans an honourable support : 
snatching out of the jaws of death the means of life 
and social comfort. 

It is, however, upon a false study or rather in an igno- 
rant and fatal reliance upon this principle, that those 
who frequent gaming-houses throw away their means, 
reputation, and life ; for the true gainers are not the 
frequenters of the gaming-table, but the keepers, who 



POPULAR FALLACIES. 205 

are acting upon this very doctrine of chances. By a 
calculation of chances it is found that in the long run, 
the keeper of a gaming house must win, in almost every 
kind of game played ; while only an occasional player, 
with what is called a marvellous run of luck, chances 
to win largely. 

The subject of probabilities, which in its right use 
is not fallacious, but is reduced to arithmetical accu- 
racy, has been placed under the general head of Fal- 
lacies, because of its being so liable to fallacious use, 
and so much employed thus. Mingling as it does with 
the superstition in our nature, we deem those things 
more probable than they are, which we desire or fear. 

The wish is father to the thought, for pleasant 
hopes : and presentiments of evil are taken for, its 
probable coming, in our gloomy periods. We give a 
rule by the use of which all this may be avoided. 

Rule. — The probability of any event is expressed 
by a fraction, of which the numerator is the number 
of chances in its favour, and the denominator is the 
sum of all the chances ; and the probability of any 
two or more events jointly occurring, will be obtained 
by multiplying together the fractions expressing the 
probability of each. 

(52.) Popular Fallacies. 

It will be well, before closing the chapter on Falla- 
cies, to show their practical use, especially in a popu- 

• 18 



206 LOGIC. 

lar illustration. A community, a state, a nation, will 
unite upon a fallacy, from which it will be a sort of 
social treason to dissent ; an age will be tinctured by 
error, pervading all classes, which only the innova- 
tion of a succeeding age can remove ; a false principle 
will cling to human nature, in the mass, during many 
centuries, which the philosophic mind can only de- 
plore in secret. 

It will be our purpose then to put forth some of 
the simplest forms of popular fallacy, beginning with 
the most general. Some of these have been already 
mentioned in their logical places, as the different 
forms of irrelevant conclusion, &c. 

I. The fallacy which is expressed by the adage, — 
Nil de mortuis nisi bonum. There is a just meaning 
to this indeed ; it is that the tongue of private enmity 
should be silenced ; that we should consider Death 
as having adjusted all difficulties as between man and 
man, and awed our mortal infirmities into a silence 
and forgetfulness of the evil which existed in him 
who is now T dead. So far the adage is good : but, 
when it becomes a principle in public morals ; when 
it tinctures the historian and the historical biographer, 
who should deal with the dead as with living defend- 
ants, arraigned for trial, its evil nature is apparent. 
When it eulogizes the dead at the expense of the 
living, and runs riot in obsequious praises and flatter- 
ing epitaphs, it assumes its most sophistic form. 



POPULAK FALLACIES. 207 

" The same man/' says Jeremy Bentham, "who be- 
praises you when dead, would have plagued you with- 
out mercy when living." The reason of this is appa- 
rent. A dead man cannot be a rival; he incurs 
nobody's envy, and is removed from all the results of 
malice. 

II. Not unlike the preceding is the fallacy con- 
veyed in the trite saying — De gustibus non est dispu- 
tandum.. This is used fallaciously to put a stop to 
controversy ; the assertion implying that as God gave 
man, each his own taste, one taste is as good as 
another. But all our systems of education teach us 
that this is not true ; that there is, on every subject 
which comes under the dictum of taste, a true stan- 
dard, which can and ought to be used. It certainly 
is better to put an end to controversy by saying that 
it is better to dhTer than to become excited and 
quarrel, than falsely to state that there can be no 
dispute about tastes. 

III. There is a fallacy which particularly assails 
patriotism : it is the fallacy of asserting that any one 
form or system of Government is abstractly the best. 
The Russian deems that men cannot be controlled in 
masses, without single autocratic power ; the English- 
man defies the world to pick a flaw in his limited 
monarchy and superb aristocracy; while the American 
boldly declares that the best government is the de- 
mocratic, representative form. Where such men as 



208 



LOGIC. 



Milton and Locke have " astonished the world by 
signal absurdities " in their models of government, we 
might be sure that its theory must be difficult ; — but 
the truth is, there is no abstract theory of human 
government. 

Asiatic barbarians, when they leave their patriarchal, 
wandering life, as in Russia, and come into the first 
corruptions of a half-civilized life, must be governed 
by despotic power ; they cannot be republican: while 
on the other hand, it is only where education is gene- 
ral among the people — that they may know their wants, 
and how to supply them, and where individual honesty 
and virtue are everywhere felt, that no undue means 
may be taken to bring about such an end, — that a 
democratic government is the right one. Then, in this 
freest form there is a reciprocal influence between the 
government and that upon which it is founded. A free 
government enlightens and purifies the people ; while 
the enlightenment and purity of the people strengthen 
and insure the government under which they live. 

IV. There is a popular fallacy, which may be called 
Sweeping classifications. It consists in ascribing to 
an individual something really belonging to another 
individual, only because the two happen to be of the 
same class ; thus, during the French Revolution, when 
the fate of Louis XVI. seemed to hang upon a thread, 
one pamphlet was issued with the title "The Crimes 
of Kings." Now, as there had been many bad kings 



POPULAR FALLACIES. 209 

in Europe, and not a few in France, Louis XVI., the 
best of them, was put into the category of condemna- 
tion, simply because he was a king. 

In times of religious revolution this has been very 
common ; as, when we hear the cry, " the cruelties of 
the Roman Catholics" uttered at a time when a bill 
for their relief was before Parliament. Former cru- 
elties in far distant countries all being thrown upon 
the shoulders of the disabled and harmless Roman 
Catholics of that day. Such, too, was the cry among 
Roman Catholics themselves in the time of James II., 
and the after Jacobite struggles, of "Protestant in- 
tolerance.'" As a further example, we refer to the 
stories circulated about the Jews, in the fourteenth 
and fifteenth centuries ; that they crucified Christian 
babes, and were guilty of secret crimes of great 
enormity. 

V. Space would fail in which to enumerate the 
current and manifest popular fallacies, most of which 
are used in legislatures and councils, and are consid- 
ered in the light of shrewd and dexterous diplomacy. 
There is the "no precedent argument." It is stated 
thus : — " The plan proposed is entirely new. This is 
certainly the first time such an idea has been broached 
in this honourable house ; and therefore, the secret 
hope is, that this house will not now entertain it." 

Next, we have personalities introduced, laudatory 
18* 



210 LOGIC. 

or abusive, by which to turn the current of the argu- 
ment. 

Another form is the assertion with regard to any 
measure, that as " no complaint has ever been brought 
against it before, it must be a good one." 

But perhaps the most insinuating form of popular 
fallacy is that by which a man is required to join one 
or the other party in every question ; thus causing the 
young ignorantly and prematurely to commit them- 
selves to views and measures which later experience 
teaches them to be wrong ; if then they change they 
are traitors or turncoats, if it be a national or political 
question ; and fickle and unreliable, if it be of a less 
general nature. It is lamentable to see party guides 
bringing those under their control forward to swell the 
ranks of their party; and those thus introduced, 
glorying in their new distinction, when self-interest 
and not truth has been the motive on both sides. 



APPLICATION OF LOGIC. 211 



CHAPTER XL 

(53.) Of certain modes in which Logic is applied. 

It is not within the scope of this work to enter 
upon the subject of applied Logic; this would re- 
quire an investigation of all the sciences, or at least 
of a very numerous classification. But it is designed 
to explain the meanings of certain phrases which 
refer to the general applications of Logic. 

We have the phrase moral reasoning, and it is 
often used as if conveying an opposite or contrary 
meaning to demonstrative reasoning. 

This has reference, not, as we have clearly shown, 
to the kind of reasoning — as there is but one — but to 
the nature of the evidence employed — the meaning 
of evidence being, that testimony which sets forth the 
truth of a proposition. Then, moral reasoning is 
the use of evidence in moral subjects, and demonstra- 
tive reasoning its use in mathematical subjects. 

Now, evidence may be of three kinds, that is as to 



212 LOGIC. 

the manner in which we obtain it ; it may be intuitive, 
inductive or deductive. 

Of Intuition, Induction and Deduction. 

We come now to consider the means of discovering 
truth, which are most useful, but which have been 
strangely confounded with Logic. They are processes 
as much bound by logical laws as all other movements 
of the reason are. 

It is evident, that in order to the Logical process, 
we must have premisses ; now, these premisses are 
obtained evidently by the three methods just men- 
tioned — Intuition, deduction, and induction or experi- 
ment. 

By intuition, we mean the absolute knowledge 
which, without any apparent effort, we find implanted 
in us. Such for example, is the aspiration of man's 
soul after a Deity, as exemplified in the religious 
systems of all people even the most barbarous, and 
such as the existence of certain affections, and notions 
of moral conduct. 

The truth of axioms is determined by intuitive 
evidence or intuition ; and in brief, consciousness in 
most of its forms, and the testimony of our external 
senses, are said to be sources of intuition. 

But most of our knowledge is derived from what 
we possess already in another form, as where we 
deduce certain inferences from acknowledged pre- 



213 

misses, or from observation and experiment, and 
generally, many observations or experiments are 
necessary before we can determine a general law; 
thus, it required centuries of observation to determine 
the Copernican theory of our solar system ; and 
almost all the developments in natural science are 
the fruit of many observations and experiments 
aggregated in each case to form one general law. 
It is an effort of man by a close study of the 
phenomena foaivopeva) or appearances of nature, to 
arrive at some degree of acquaintance with the 
noumena (voovfisvaj or essences of its objects. 

To unite these was the aim even of the heathen 
philosophers, and with their obscure lights they worked 
ardently in the labour ; it remained for a doubter 
(Sextus Empiricus), two centuries after the coming of 
Christianity, to connect them for another purpose, 
and that was to arrive at a suspension of all judg- 
ment on objects whose nature is obscure, and thus to 
acquire a certain repose of mind (a^apalta), and perfect 
equanimity of disposition (^ptorfaflfta). But the in- 
ductions of Sextus were never really performed ; he 
theorized to his scepticism, and his theories will not 
bear the rude hand of physical practice. 

In order to illustrate the difference between in- 
duction and deduction, let us suppose a law already 
determined, which we state in the proposition A is B. 
Let any number of particular examples, as x, y, z, 



214 LOGIC. 

range tinder this law, thus, x is A, j is A, z is A., 
and wo can manifestly reach the conclusion that x, 
y, and z, are all and severally B. 

But suppose the general law unknown, and that it 
be approximated to in proportion to the number of 
particular examples ; we shall thus have x is B, y is 
B, z is B, &c. ; but x, y, z, &c, as we increase the 
number of the examples, represent the class A ; hence 
we may state the law A is B : the truth of which 
will depend upon the number and extent of the expe- 
riments performed and particular instances observed. 
Or, to recapitulate in syllogistic form : — 

Deduction. Induction. 

(Law) A is B. (Part, examples) x, y, z, &c, are B. 

(Part, examples) x, j, z, &c, are A. A is tbe class to which x, y, z, &c. belong. 

(Conclusion) x, y, z, &c, are B. (Law) A is (likely to be) B. 

Now there are certain sciences in which, from the 
nature of things, we can never state more certain re- 
sults from induction than this likelihood; but this 
likelihood, it must be observed, becomes greater and 
greater, and at length touches absolute certainty, 
when we examine many particular instances and find 
none of them failing to range itself under the law 
which we call likely. So that at the last we write it 
to all intents and purposes as a categorical proposition, 
A is B. In some sciences we may exhaust all the 
particular examples and finish our induction by a 
certain law. This induction has led, as the other 
could not, to certainty. 



215 



There are two kinds of induction, material and 
formal; and it is by a want of proper distinction be- 
tween them that the error has arisen of comparing 
induction improperly with the syllogism, and asserting 
that while induction is one kind of reasoning, the syl- 
logism is another, i. e. deduction. 

Hence Lord Bacon and his followers, finding that 
deduction generally moved from what was contained in 
known premisses to lower classes or individuals con- 
tained in them, threw aside the syllogism as useless, 
and inaugurated induction as the new Logic of experi- 
mental philosophy. A simple examination of material 
and formal induction will set us right. Material in- 
duction is the process of experiment and observation ; 
the laborious investigation of facts, as to their dis- 
covery and their combination ; but formal induction 
is obtained by the use of the syllogism itself: not 
confined, as some writers have attempted to show, to 
the third figure, but in most examples capable of being 
at once written out in the first figure, the form in 
which they may be immediately tested by the dictum 
of Aristotle ; as in the example : — 

/if/ri' -n Whatever is true of the cow, goat, deer, &c, is likely 

to be true of all horned animals ; 
Min. prem,. Rumination is true of the cow, the deer, &c. ; 
Concl. (Law). Rumination is likely to be true of all horned animals. 

The naturalist receives this as the only just con- 
clusion from the formal induction to which the syllo- 
gism has helped him; but, having as yet found no 



216 LOGIC. 

exception to the rule, he writes it out boldly and 
without fear of contradiction, 

All horned animals are ruminant. 

Of certain modes of using Syllogisms. 

Argument a priori. — This is the mode of passing 
from known antecedents, to necessary consequents ; 
or, in the sciences, from cause to effect. Thus, if we 
consider the being of a God and of his attributes to 
be independently known, as by intuition, then we rea- 
son a priori to the existence of his works, the univer- 
sality of his providence, and the gracious designs of 
his redemption ; this reasoning is most plainly stated 
in the form of the constructive conditional syllogism ; 
the affirmation of the antecedent — or cause — helping 
us to the affirmation of the consequent — or effect. 

Argument a posteriori. — This is reasoning from 
effect to cause. If, by an inverse process, we first study 
natural religion, and experiment upon the wonders 
of the human mind, and then pass back from these 
works around us to the establishment of the existence 
of a first great cause, who must have made them all, 
we are said to reason a posteriori, or from results to 
their causes. 

Of the two modes of reasoning, both are useful 
and effective, but the reasoning a priori is the most 
certain, and analogous to deductive inference, while 
the reasoning a posteriori must always have some un- 



MODES OF USING SYLLOGISMS. 217 

certainty akin to the processes of induction. For if 
the argument be placed in the conditional form, as 
before, we have really no right to pass from the affirma- 
tion of the consequent, to the affirmation of the antece- 
dent. It is usual, therefore, to limit the conditional in 
reasoning a posteriori, so that the consequent in ques- 
tion must be considered to spring from that antece- 
dent, and no other. 

History uses both forms, and combines them with 
great success : taking, for example, on the one hand, 
the early elements of a nation's life ; its people, its 
geography, its tendencies of government — history 
seeks to trace these to their legitimate results among 
the changing scenes of national existence ; while on 
the other, looking around at the present condition and 
conduct of a nation, she takes these results, and tracing 
them back, in careful combination, with each step re- 
moved from the present, she seeks for their early and 
prime causes, in the classic times of the country's 
origin. 

There are, it must also be observed, certain results 
of a spiritual kind, both in natural and revealed re- 
ligion, which may be justly reasoned upon a posteriori, 
to their certain causes and source. Such, if we mis- 
take not, is our Saviour's teaching, when he declares, 
"by their fruits ye shall know them:" asserting the 
exact analogy between the fruits of the Spirit and the 
19 



218 LOGIC. 

fruits of vegetable life. Since certain events of which 
we are aware, while yet their causes are unknown to 
us, may have sprung from any one of several causes, 
we must be careful upon what subjects and to what 
extent we use the a posteriori mode of reasoning, for 
even when it seems most applicable, it may fail us. 
Thus, if in time of yellow fever we should see a man 
suddenly sick, and should assert, 

This man is sick, 
Therefore, He has the fever ; 

it might prove an exceptional case ; he might be sick 
of something else. This is a very open and familiar 
illustration, but serves to indicate the dangers to which 
it is liable. Almost all the processes of discovery in 
natural religion are by means of the reasoning d 
posteriori. 

Argument a fortiori. — This is a method by which 
we establish a stronger conclusion even than ordinary 
premisses need to warrant us. Thus, 

A is greater than B. 
B is greater than C. 
A is greater than C. 

That this conclusion is just there can be no doubt ; 
and that the form of it is not exactly that of the regular 
syllogism, is equally apparent. 

Hence, some writers have denied that it is a syllo- 
gism, or can be put at once into syllogistic form. 



MODES OF USING SYLLOGISMS. 219 

Easily to demonstrate the error of such, let us trans- 
pose the apparent premisses, thus : — 

B is greater than C. 
A is greater than B. 
A is greater than C. 

And replacing {greater than Q) by X, we shall have 

BisX. 

A is B (because it is greater than B). 

AisX. 

This conclusion is a comparative proposition which can 
be at once shown by replacing X, by its value, (greater 
than C). 

This reasoning a fortiori is very effective and 
proper ; and was used by our Saviour in his invectives 
upon Chorazin, Bethsaida and Capernaum, with 
thrilling effect. So also is it forcibly used by the 
apostle, to the Hebrews (x. 28), in the words : 
" He who despised Moses' law, died without mercy 
under two or three witnesses : of how much sorer 
punishment shall he be thought guilty, who hath 
trodden under foot the Son of God," &c. 



220 LOGIC. 



CHAPTER XII. 

A HISTORICAL SKETCH OF LOGIC. 

(54.) Division of the Subject 

Having completed, in general outline, the study of 
the formal Logic, in its present condition of exactness 
and practical use, we are ready to go back to its 
feeble beginnings, and trace it in its slow and tram- 
melled movements from the days of the early Greek 
Philosophy, through the applications of Roman 
Science, the enlightening process of Christianity, the 
darkness of the scholastic subtleties, the dawn and 
advance of Experimental philosophy and the meta- 
physics of the eighteenth century, down to the con- 
troversies of our own day. 

Nor are we yet to regard the science of Logic as 
established beyond dispute, and fairly stationed among 
its sister sciences ; it is yet an arena of dispute, and 
the most distinguished philosophers disagree, as has 
been seen, even as to what it is, and as to what is its 
scope. 



HISTORY OF LOGIC. 221 

It would be of great interest and profit to take 
such a historical view in detail ; but the limits of this 
work will not permit it, and, besides, for all practical 
purposes, the periods of the history naturally divide 
themselves into four. These so much transcend all 
others in interest and value, and so absorb the events 
which just precede or immediately follow them respec- 
tively, that they form the plainest and most conve- 
nient method in which to present the History of Logic. 
They may be marked by the titles — 

1. Aristotle. 

2. Christianity and Logic. 

3. Bacon, and the rise of Inductive Science. 

4. The present system. 

1. Under the first may be classed all the efforts of 
the human mind in the arrangement of a canon of 
reasoning, in that early time when knowledge, preced- 
ing method, was only seeking in darkness and ob- 
scurity that system of laws and principles by which 
alone knowledge may be made available. Around 
Aristotle, too, cluster the great expansions of science 
which were due to the conquests of Alexander, and 
the great kingdoms of his successors. 

2. In the coming of Christianity, Logic found not 
a rival, but a guide, and in the early church it was 
the weapon of their spiritual warfare. To the church, 
as the representative of Christianity, is due much of 
the error as well as the good of scholasticism. 



222 logic. 

3. Logic was the servant, the ill-used servant of 
Inductive philosophy, and owes much of its long bon- 
dage and oppression to the illustrious founder of the 
system of Experimental philosophy. 

From these considerations, it has been assumed that 
we are better able to look into this history now that we 
are acquainted with the scope of the science ; otherwise 
we might fall into the same error, by reason of the 
honourable company in which we should find ourselves. 

4. Since the time of Lord Bacon, and perhaps by 
reason of his example in condemning the syllogism, 
Logic has been degraded from its position as the con- 
troller of the reason on all subjects, and has been so 
intermixed with Mental philosophy as quite to lose its 
identity, and be miscalled by its own name. This was 
its condition during the eighteenth century. In the 
nineteenth there have sprung up many champions of 
Aristotle and the syllogism, among whom first in dis- 
tinction is Archbishop Whately. The universal prin- 
ciple of reasoning has been rescued by him from obli- 
vion and degradation ; and Logical science, although 
still maligned and fiercely attacked, seems ready to 
take its permanent place among the great Elemen- 
tary sciences of human investigation and instruction. 

(55.) Aristotle. 
It must be considered that the progress of such a 
science as Logic was necessarily gradual and slow ; 
that from the beginning, men had been contemplating 



ARISTOTLE. 223 

the operations of the reason, or were making vain but 
progressive efforts to distinguish the exact functions 
of the reason, among the mazy elements of the human 
intellect. Many men had collected much material, 
which lay floating in a chaotic state upon the great 
deep of the human mind. 

The logical doctrines of conception as expressed 
in terms, of judgments as formed in propositions, were 
known to Socrates and Plato. Indeed, Zeno the 
Eleatic, who is mentioned as the inventor of Dialectic, 
had invented logical puzzles which required an inves- 
tigation of the laws of thought, and that caused a 
race of so-called teachers of Dialectic to spring up 
in Greece. 

So the first movements in Logic were trammelled 
by the ignorance and empiricism of those who called 
themselves teachers. 

The experience of our own age has taught us that 
true science is more impeded and injured in this than 
in any other way. A whole class of speculative logi- 
cians in the early times went by the name of Sophists. 

We are accustomed to hear the Sophists spoken of 
in terms of contempt, and sophistry has come to mean 
Fallacy. But we should err very greatly, as many 
in all ages have erred, if we regarded them as wholly 
evil. The most enlightened writers of modern times 
have demonstrated, that much of the odium which 



224 logic. 

attaches to the name, belongs really to the abuse of 
their art; they were paid teachers, — among whom 
are enumerated Protagoras and Gorgias, — whose duty 
was to train up young men for the duties and pursuits 
of public life. The character of the Greeks, who 
were fond of riddles and disputes, and the errors of 
the age, led to their real sophistry ', and their abuse of 
the rhetorical art to make " the worse appear the 
better reason;" after that, their efforts were not for 
the purpose of widening the range of knowledge 
and truth, but really served to check these, and thus 
give a free course to fallacious reasoning. 

The Logic of Euclid consisted in negative proofs ; 
his design was, in encountering an opponent in con- 
troversy, not to attack his premisses, but his conclu- 
sion. 

Chief among the early logicians, as he is distin- 
guished among the sages of the world, was Socrates. 

Much interest and sympathy attach to the virtuous 
and heroic life, and the tragical fate, of this wise and 
good man ; but it is principally by his philosophy and 
logic that he has been useful to the world. Keeping 
in view always before his numerous scholars, the 
dignity of Logic as a science, and the loftiness of the 
reasoning powers, he guided the logical processes by 
what is now called « common sense." " This is implied 
in Cicero's declaration, that Socrates brought philo- 



ARISTOTLE. 225 

sophy from Heaven to earth. Xenophon, likewise, tells 
us in his « Memorabilia,' that when he wished to 
form a decision on any subject, his reasonings always 
proceeded from propositions generally assented to or 
understood."* Condemning the errors into which the 
Sophists had been led, he claimed Truth as the real 
aim of reasoning, and established in all his arguments 
a high principle of moral responsibility. The analytic 
process was that mainly employed by Socrates ; and 
thus, when Plato appeared, he found the science of 
Logic, and the art of Dialectics, presented by de- 
tached and isolated views, as the result of previous 
investigations. The analysis had only prepared for 
the synthesis. 

The plan adopted by Plato was the Synthetic 
method, and by this he worked out many great results. 

Perhaps the best feature in the Logic of Plato was 
that on approaching the science, he tells us to keep 
the mind free from all preoccupations and preconcep- 
tions : he declared, as an axiom, that « Ignorance is 
the true start point for Science." Disputing the asser- 
tion of the earlier philosophers that sensation was the 
foundation of truth, he proved it to be one of the 
instruments by which truth is arrived at. Without 
stopping to give a sketch of his system, we may state 
that his Logic and theology are so intimately con- 
nected, that we may judge of the vigour of the one 

* Blakey's Historical Sketch of Logic, p. 24. 
P 



226 logic. 

by the developments of the other. He proved the 
existence of a Deity, who was the measure of all 
knowledge, the centre of all truth ; and in mysterious 
language he declares that this centre is " the begin- 
ning, middle, and end of all things." But Plato was 
to be eclipsed by a greater mind ; in fact one of the 
greatest minds the world has ever seen. 

When much material was thus collected, when 
many vague theories had thus been started, and when 
crowds of ignorant pretenders had arisen to be con- 
verted or silenced, Aristotle came to create a new 
system — to enlighten, to harmonize, and to sweep away 
all the errors of the Dialecticians and the Sophists. 
He, who was to correct the characteristic errors of 
the Greek philosophy, was himself a Greek. The 
Greek mind was eminently a curious one. All the 
speculations of philosophy, all the systems of Ethics, 
were directed apparently and nominally indeed to the 
discovery of truth ; but if they reached, by specious 
arguments, a pleasant conclusion, it mattered little 
for pure truth. They contented themselves with the 
fruits of their system, once that system was estab- 
lished. 

The Athenians were characterized by the apostle 
as " spending their time in nothing else" but the pur- 
suit of novelty ; and they were but the types and 
representatives of the other states and cities of 



ARISTOTLE. 227 

Greece. There are in the early Greek authors many 
corroborations of the apostle's assertion. 

Aristotle, building upon the combined foundations 
of Socrates and Plato, discovered many new princi- 
ples and established new rules, until he had elaborated 
the system of Logic which we have at this day. 
His Logical works, published in full under the title 
of "Aristotle's Organon," comprise the following 
works : 1. The Book of the Categories ; 2. Of In- 
terpretation ; 3. The Prior Analytics ; 4. The Post 
Analytics; 5. Topics; 6. Of Sophisms. 

Of these, the most important are " The Book of the 
Categories," and both "Analytics." We shall pro- 
ceed directly to explain their meaning. 

He drew the true and somewhat nice distinction 
between Logic and Rhetoric, and established the fact 
(a fact not yet learned by many who call themselves 
logicians) that Logic is not concerned with the truth 
of propositions, but only with the reasoning upon 
such propositions as are given into its charge. If 
the premisses be true, then Logic will give a true 
conclusion ; but if the premisses he false, Logic gives 
a false conclusion ; but in this latter case the Logic 
is as good, the argument as valid, as in the former. 

In establishing his dictum, which we have assumed 
to be the universal principle of reasoning, he laid 
down the general law of Logic, a law which has been 



1-: LOGIC. 

misunderstood and misinterpreted, for this dictum 
was not a model for common arguments, but simply a 
test for all. 

: the Greeks looked for truth and found that 
Logic did not impart it ; that before Logic could be 
used they must be possessed of premisses, which pre- 
i ~ere given them either by intuition or by 
observation, i. e.. induction. — they either abused Logic 
for not doing what it could not propose to do, or else 
injured it much more than their abuse could do, by 
using it as a vehicle for false philosophy and mythic 
religion. They took, to save themselves the trouble 
of laborious induction in search of premisses, the 
vagaries of their own quick, joyous and disputatious 
minds, and thus produced monstrous and absurd con- 
clusions, which, since their Logic was valid, they felt 
satisfied to consider as true. 

The union of this Grecian spirit with the equally 
va^ue and fantastic imagination of the Orientals, with 
whom by conquest they became acquainted, further 
corrupted their intellects, and robbed Logic of its 
true character and mission ; leaving the whole domain 
of Philosophy without the true guide of Reasoning. 

Le: us now look in turn at the logical works com- 
prising the Organon. 

The Categories. 
^e are in the habit of using the word category: for 



ARISTOTLE. 229 

example, we speak of a person or thing being put in 
this or that category ; the word and its use we owe to 
Aristotle. His categories are ten in number. They are 
not all now considered of importance in classification, 
but are still worth an explanation, as the original sys- 
tem, from which, by careful elimination, we have pro- 
duced our own later classifications. The categories 
were supposed to imply answers to all possible ques- 
tions concerning a term, expressing an act of appre- 
hension : i. e., all of which we can have any knowledge. 

1st, Substance. 2d, Quantity. 3d, Quality. 4th, 
Relation. 5th, Action. 6th, Passion. Tth, The 
Where. 8th, The When. 9th, Position, in space. 
10th, Possession. 

The categories may be thus more fully ex- 
plained : — 

1. Substance may be defined that which is in itself, 
which may be conceived as existing by itself. This 
is divided into spiritual and temporal ; and subdivided 
according to classes, genera, species, &c. 

2. Quantity may be translated liow much, or 
how great, and by implication, as to time, how long. 
Thus, under the head of Quantity, we have the three 
special considerations of Number, Magnitude and 
Time (as to duration). Number, we know, is either 
abstract or concrete, as when we speak of a number 
disconnected with any objects, or, of a number of 

20 



230 LOGIC. 

objects or things. Thus, quantity, as a category, covers 
the science of arithmetic. Magnitude is either linear, 
superficial or solid ; and thus its genus quantity cov- 
ers, likewise, the science of geometry. Time is either 
permanent or successive, and is used to indicate the 
movements or conjunctions of Number and Magni- 
tude. 

3. Quality describes the kind or sort of which a 
thing is ; and is subdivided into Habit, or a quality 
induced by frequent repetition of the same act, as 
virtue, vice, &c. ; Inherent nature, as man's reason : 
From these grow the many subdivisions of colour, 
Sound, hardness and shape. 

4. Relation is the consideration of two or more ideas 
with reference to each other. The first idea of two, 
is called the relative, the second the correlative, as 
prince and subject : master and servant. 

5. Action has a double meaning : it is at once the 
exertion of power by one body on another, and the 
effect produced by such an exertion. 

6. Passion is the endurance of another's action. 

7. The Where includes the three meanings which 
we express by the words where, whence and ivhither : 
as in Philadelphia, from New York, to London. 

8. The When has reference to the exact period 
of time, and not its duration, which, as we have seen, 
belongs more properly to quantity. The When may 



ARISTOTLE. 231 

be expressed by the phrases to-day, to-morrow, a hun- 
dred years ago. 

9. Position has reference, not to the place where, 
but to the posture in which a body is found, as lying 
down, standing up, kneeling, &c. The question then 
is, how did you find it ? not where f 

10. Possession has reference to something belong- 
ing to the object, or placed upon and clothing it ; and 
as a category, covers all questions concerning the 
rights of property. 

Of these categories, it will appear that substance 
stands apart from the rest, in that it is sensibly exist- 
ent, and they are all attributes of such an existence ; 
It will further appear, upon examination, that Quan- 
tity and Quality are essential attributes, i. e., belong 
to the essence of the object necessarily ; while Rela- 
tion, Action, Passion, The Where, The When, Posi- 
tion, and Possession, are accidental circumstances 
which may be dissociated from it. 

To render this clearer, for facility of reference, we 
state it in a tabular form. In this table we place all 
the explanatory parts as by the rules of division be- 
fore given, but number the categories, that the eye 
may at once rest upon them. 



232 logic. 

The object or existence expressed by a term. 



Attributes belonging 
to the substance. 






1. Substance. 


Circumstantial. 






Essential. 


1 
4. Relation. 


2. Quantity. 


3. Quality. 






1 
Number. 


Magnitude 


. 1 

Time. 1 




r 
Habit. 


■ 

Inherent nature. Shape, &c. 


1 

5. Action. 6. Pa 


1 

ssion. 7. 


1 

The Where. 


1 
8. The When. 9. 


1 1 

Position. 10. Possession. 



Aristotle asserted, that everything which could be 
said of any subject is included in one, some, or all of 
these categories, and his own illustration of their use 
is one of the simplest which can be found. It was as 
follows: — "Substance, man; Quantity, one; Qua- 
lity, white ; Relation, greater; The Where, in the Fo- 
rum; The When, yesterday ; Position, sitting ; Ac- 
tion, whatever he may be doing ; Passion, whatever 
may be being done to him." 

It is under this first attempt at method, that the 
sciences began to range themselves in classes, and by 
this all other systems of classification seem to have been 
suggested. Thus : Substance is the foundation of all 
Physical and Historical investigation : Quantity, the 
subject of Mathematics ; Quality, of Medicine; Rela- 
tion, of Ethics ; Action and Quantity, of Astronomy, 
Music and Mechanics : Passion and Action, of Elec- 



ARISTOTLE. 233 

tricity ; the Where, of Geography ; the When, of 
Chronology ; Position and Quality, of Sculpture ; 
Habit and Position, of Painting : and so each art and 
science would be found to range under one of these 
singly, or more than one, when combined. 

The books of « Prior and Post Analytics" originate 
and develop his system, of the doctrines and use of the 
Syllogism. They have been the resort of all writers 
on formal Logic since his time, and there has been but 
little alteration in his method. Aristotle established 
but three figures of the syllogism, the fourth being 
afterwards added by Galen. 

In his book of Topics, he discusses the subject of 
Predicables, or Glasses, and establishes the expression 
of a predicable to be in four ways, i. e., by genus, 
differentia, property, and accident: in these he im- 
plies the species, since we have seen that if we add 
the differentia to the genus, we obtain the species. 

In his book of Sophisms he states thirteen Fallacies, 
as including all those which can bear a syllogistic 
form. Six of these refer to the words used, and are 
called Fallacies in dictione, and seven consist in the 
matter of the propositions, and are called Fallacies 
extra dictionem. 

The logical works of Aristotle seem to have been 
providentially preserved. Transmitted by his dis- 
ciples from hand to hand, they were at length con- 
cealed in a vault during one hundred and thirty years, 
20* 



234 logic. 

until they had mouldered into an almost illegible con- 
dition. Restored from this condition, they came by 
the fortune of war into the hands of a Roman gene- 
ral, and thus were given a second time to the world. 

We cannot pause to notice all the changes attempted 
in Logic and Philosophy from this time until the Chris- 
tian era. After the Peripatetics, came Pyrrho of Elis 
and his Sceptics, who seem to have employed Logic to 
deny the possible attainment of pure truth. They 
embodied their system in Ten Tropes, or logical rules 
for the government of mind in the search of truth. 
Their doubt led to what they termed a suspension of 
judgment, rather than a positive denial. 

Of the Epicureans and Stoics, it may be said that 
they aimed at the establishment of no Logical system, 
but rather a few tenets in the shape of propositions ; 
by these, as doctrines, they guided their course. 

The tenets of Epicurus may be comprised in the 
assertion that " whatever is useful, pleasant and de- 
lightful, is true." This is to assert that man's senses 
and bodily appetites are the only test of truth. These 
have been called his " emotional criteria." 

The Stoics rejected the categories of Aristotle and 
adopted four of their own : and attained the conclusion 
that "pain is no evil:" a philosophic stretch of the 
imagination which has given its name to an unshrink- 
ing endurance of pain and evil. 

Very little transpires concerning Roman systems 



AKISTOTLE. 235 

of Logic. Although Cicero, Maxinms of Tyre, and 
Gralen lay claim to the title of logicians, the logical 
system of Aristotle was adopted by them all : 
Rhetoric became the more valued and important 
study. 

The history of Logic, then, from the time of Aris- 
totle to the coming of Christ, is not a history of 
change ; but the logic of Aristotle, however unchanged, 
had been most unworthily used. No longer the guide 
and test of just reasoning, it became the vehicle of 
ingenious falsehood, was made to support any theory, 
and gave power to its possessor " to argue on both 
sides of any question." To satisfy curiosity it estab- 
lished any paradox, and one being made the premiss 
to another, the error was multiplied " in infinite pro- 
gression undefined." It was not the logical system, 
but the mind of man, which needed purification : not 
abstract propositions, but the matter they contained, 
which demanded scrutiny. 

We shall see also that the misconception of the 
sphere of Logic was equally fruitful of error long 
after the establishment of Christianity, and that it 
has remained for the nineteenth century, notwith- 
standing the utmost resistance of many learned but 
dogmatic philosophers, to give to Aristotle and his 
system their true place in the domain of science : an 
instauration, not by one man ; a new Organon, not 
the product of one teeming brain, but the tribute of 



2?>G LOGIC. 

Philosophy, inductive and, deductive, to Aristotle, 
the great founder and framer of that system which 
alone controls the unbridled reason, and sends pure 
truth into the channels of usefulness and practice. 

But, meanwhile, the coming of Christianity was to 
produce great marvels in the domains both of Logic 
and Philosophy. 

(56.) The Logic of Christianity. 

The Logic of the Grecian schools had been the 
guide of man's Reason, but now it was itself to be 
brought into companionship with a higher human 
attribute, Faith. Premisses were no longer to be 
sought by the ordinary means of evidence, but to be 
supplied in a new and marvellous manner. Chris- 
tianity combined this new element with Philosophy, 
and taking the art of Logic as the vehicle of its 
great truths, used it in a manner at once beneficial 
and practical ; putting an end, as it seemed, to the 
controversies and paradoxes which had beguiled and 
engaged the Greek and Roman mind. 

By this new tutelage of human reason, Christianity 
produced an immediate and startling change in Philo- 
sophy, by opening the Finite upon which man may 
use his reason, as well as indicating the Mysterious 
and Infinite to his faith. 

As much as we may despise the Greek systems of 



LOGIC OF CHRISTIANITY. 237 

speculative Ethics, upon which they employed their 
nobler Logic, we must remember that they were the 
gropings of men in the dark, pursuing a faint glimmer 
of light in the hope that it would lead them into the 
full sunshine and free air of Truth. They had no 
revelation of intelligible fact or of mystery. The 
efforts of Plato to attain to different degrees of know- 
ledge which he calls — "the absolute, the probable, 
the imperfect," the Politics and Ethics of Aristotle ; 
the bold dicta and quiet endurance of the Stoics ; 
the "emotional criteria of Truth," propounded by 
Epicurus, and so much abused by his disciples, — were 
all vain attempts to arrive at that knowledge which 
could come to man only by miraculous revelation. 
God vouchsafed no such revelation to them ; it is no 
cause of wonder that they erred greatly without it. 

This, then, was the crowning glory of Christianity, 
that it gave to man pure Truth, and furnished him 
with a world of new facts upon which to reason, of 
glorious propositions upon which to try the powers of 
his Logic. The language of God to man, was, first, 
" Come, now let us reason together," and thus the 
whole system is based upon reason ; and afterwards, as 
if thus founded surely and safely, « Believe, and ye 
shall be saved." 

Unlike the Greeks, the Jews had always possessed 
this revelation, in a ceremonial and progressive form. 
Their own Scriptures had disclosed to them not only 



238 logic. 

the true story of man's origin and fall, but of God's 
supremacy, and his gracious design of restoration, 
and their prophets had told them with a heavenly 
Logic of Type and Symbol ; premiss upon premiss in 
glorious abundance, of that certain conclusion, the 
advent of the Messiah. 

The "fulness of time" came, and the event fulfilled 
the prophecies, the conclusion completed the pre- 
misses. Christianity brought philosophic as well as 
religious light. 

By a strange infatuation, they who had thus awaited 
His coming, refused Him when He came ; and since 
He could not be the glory of His earthly " people 
Israel," He was, in a truly philosophic sense, " a light 
to lighten the Gentiles." 

In three centuries, He had been eagerly embraced 
by Heathen Rome, and the Logic of Aristotle, freed 
from its vile and improper uses, and used as the 
propounder of a full and pure creed, was applied with 
great power to the spread of the Christian religion. 
Where false premisses had been ignorantly used, lead- 
ing to a false conclusion, or where false conclusions 
had been improperly deduced from true premisses, 
everything for a time was changed. Truth was every- 
where triumphant, and its reign seemed to be eternal. 

Such was the first influence of Christianity upon 
Logic. Containing in itself nothing repugnant to 
reason, it gave a host of new and glorious truths, 



LOGIC OF CHRISTIANITY. 239 

fresh from the mouth of God ; it simply threw away 
the vague speculations, the unsound paradoxes, which 
had been heretofore used as premisses, and took these 
new truths to reason upon. In the teachings of our 
Saviour and the apostles, it need scarcely be remarked, 
not only that every statement is true, but that every 
argument is valid. 

On the other hand, Logic, turning gladly away 
from the subtleties and absurdities of mythical phi- 
losophy, pressed forward with ardour in the task of 
systematizing and promulgating the new doctrines of 
Christianity. 

In this manner arose the logical systems of the early 
Christian writers and apologists, known as " the 
fathers." There is, indeed, error to be found in their 
'uninspired writings, such as we should expect in all 
human productions, but from Justin Martyr to St. 
Augustine, one object of their writings seems to have 
been the harmonizing of Christian doctrine with the 
Logic of Aristotle, and thus while they preached the 
truth, to show at once the union and true relation of 
Reason and Faith. How well they succeeded as a 
class, may be seen at the present day from the grow- 
ing interest in their writings which is manifested by 
all who are interested in Religion or Philosophy. 
Never forgetting that they were surrounded by enemies 
and error, one part of their works was fiercely contro- 
versial, always keeping in view the elenchus, and 



240 LOGIC. 

warily observing an opponent, or rather the many op- 
ponents who were scrutinizing their deeds and words. 

Where, in the old system of Philosophy, Sensation 
was the starting point, and man must evolve philoso- 
phy from within himself — they established Revelation 
as the centre and starting point, and would draw, by 
the same logical formulae, all true philosophy from 
God. From this time, Logic was inseparably con- 
nected with theology: the Church ruled the world. 

The Christian Church had, in its union with the 
Roman empire, a strength and stability from which 
great philosophic results must have sprung; but just 
when they were framing this glorious system at once 
of Religion and Philosophy, the Roman empire of the 
west fell, under the ruthless attacks of the Northern 
barbarians, and the Church was temporarily paralyzed 
by the shock. For centuries after, the great efforts 
of the Church w T ere directed to the attainment of a 
firm social basis, and political power. 

We have already stated the connexion between 
Logic and Philosophy. They may be dissociated, but 
are both then useless. Thus, indirectly, Philosophy 
has exerted such an influence upon the uses of Logic 
that it is important to trace the systems with which 
Logic was combined, and to promulgate which it was 
used after the establishment of Christianity. Most 
of the Christian writers investigated the subject of 
the human reason, and studied the Logic of Aristotle. 



LOGIC OF CHRISTIANITY. 241 

As might be expected, so magical a transformer as 
Christianity was not without fierce philosophic oppo- 
sition. With equal steps Scepticism and Heresy ad- 
vanced. Those who were doubters before where only 
Science was concerned, were doubly doubters when 
told of Christian mysteries. 

The representative of the new sceptics was Sextus 
Empiricus, who lived in the beginning of the third 
century, and who was but a new incarnation of Pyrrho 
of Elis. Unwilling to receive, on prima facie evi- 
dence, the truth of the new revelation, they had 
fallen back upon the old material, and had worked to 
the same results as the Greek philosophers ; they 
turned their backs on the light, — which admits of no 
better proof than the physical light of day, — and 
walked into the cave of darkness, of doubt, and, in a 
religious view, of despair. 

The scepticism of Pyrrho, three hundred years 
before Christ, was consistent, and well deduced when 
compared with this, and yet the Greek academicians, 
we know, had convicted him of absurdity. « Be- 
cause everything is contradictory, everything is false." 
Now, if this be true, the axiom itself is false, and so 
the sceptic, thrown upon the horns of a dilemma, must 
grope again, in vain, for new proofs of falsehood, and 
new certainties of doubt. 

Of the Neo-Platonic, Eclectic or Alexandrian 



242 logic. 

school, the object; seems to have been to unite the 
Greek philosophy and Oriental dogmatism into one 
system; but it was a false and feeble combination, 
fated to a speedy and ridiculous end. 

Its metaphysics, as prepared by Plotinus, was the 
attempt by the combination of heathen obscurities to 
attain to Christian light; its theology, as reduced by 
Iamblichus, was a strange retrogradation from the 
Scriptures, which revealed the person and word of 
God, to the ridiculous deities of the Pantheon; and 
its Logic, of which the great Porphyry was the ap- 
plier, was an attempt, by the use of the Aristotelian 
system, to establish all theBe errors, at the expense 
of the fair fame and even of the existence of Logic. 

Nor in the singular applications of Christianity to 
Logic must the Gnostics be forgotten. Their name 
indicated their creed ; yvaoi$ f knowledge, as opposed to 
faith : Naked Logic, stripped of its armour, was made 
again to do duty in the ranks of the Prince of Dark- 
ness. Gnosticism " took such portions of the Gospel 
as suited its views or struck its fancy; but these rays 
of light they mingled with such a chaos of absurdity, 
that the apostles would hardly have recognised their 
own doctrines."* 

The greatest, perhaps, of the indirect evidences of 

* Burton's "Heresies of the Apostolic Age," p. 15, quoted by 
Neil. 



LOGIC OF CHRISTIANITY. 243 

the truth of the Christian religion is, that in spite of 
the false systems which sprang up to oppose it, it has 
steadily and mightily prevailed ; in its progress it has 
purified human philosophy, and unfettered Logic; 
but it did not accomplish this without fierce contests ; 
it was to come upon dark days, in which it was the 
only glimmer of light ; days in which the misuses of 
Logic were no longer to be confined to profane sys- 
tems or heretical creeds. Unfortunately, they are 
constantly found in the career of the Christian Church 
herself. As an institution designed to convey Chris- 
tian truth to all generations, it would be supposed 
she could have little to do with the conflicts of the 
world around her. Not so. As soon as the Church 
was struck with the ambition for power, the lust for 
empire, she began to pervert facts and degrade Logic. 
The days of the truthful and zealous Fathers had 
given way to that of ambitious prelates, and greedy 
ecclesiastics of every degree. It was the dark age 
of Logical Philosophy. As long as she was weak, 
and feared lest the brute force of kings and barons 
should crush her power, and check her increasing 
influence, she asserted the difference and distinction 
between the secular and spiritual; and thus main- 
tained herself as the spiritually strong ; but as soon 
as she had acquired strength and control, in her spi- 
ritual capacity, she claimed a share in temporalities, 



244 logic. 

and put her strong hand upon all the kingdoms of the 
world : she usurped the power and province of her 
divine Master, and said, " By me do kings reign, and 
princes decree justice." 

Claiming infallibility at first, only in doctrine ; at 
length, in general opinion; she trammelled science, 
expurgated literature ; controlled, or attempted to 
control, the thoughts of men, and placed the gaunt- 
leted hand of despotism upon philosophy, demanding 
that it should speak only at her will and by her 
dictum. It was an evil day for the Logic of Aristotle, 
when this corrupt Church claimed it as the frame- 
work of her ethical system, because she used it only 
to draw from false premisses, false conclusions. It 
was a happy thing for the Church that Logic did not 
look beyond the form of the expression, or her ma- 
chinations would have been more thoroughly exposed. 

Assuming premisses slightly false, the Church rea- 
soned to conclusions monstrously false. From 'probable 
premisses, it arrived at certain conclusions : and not 
unfrequently was it guilty of Logical fallacies, as 
well as Material. A slight and cursory examina- 
tion of the sophistries of the Church in the Middle 
Ages, would show us how Logic was degraded and 
misused ; but we shall content ourselves with a few 
words upon the rise and progress of Scholasticism, 
the form which seems, in its changes, to present at 
once the Philosophy and the Logic of Christian 



LOGIC OF CHRISTIANITY. 245 

Europe in the Middle Ages. That the Church should 
have espoused the formal Logic of Aristotle was not 
entirely without good: for as the Church espoused 
it, it became a popular science in the new schools 
which arose wherever the Church went. Thus arose 
in the foundations of Charlemagne, the Schoolmen, 
whose object was to connect or harmonize the elements 
of all truth which remained to man after the fearful 
convulsions in the Western Empire ; a restoration 
in Philosophy similar to that of Charlemagne in do- 
minion. 

The duty of the Schoolmen seems to have been to 
determine what was Philosophy, and how much it had 
to do with Religion. In such a question Philosophy 
would surely hide its diminished head. Distinguished 
Popes, like Gregory the Great, were for proscribing 
all secular studies, and making theology the only study 
of the world : — in order to effect this purpose, we 
know that he destroyed valuable manuscripts. A host 
of mad enthusiasts, called Saracens, had destroyed a 
wealth of history and science in the library of 
Alexandria ; but the very darkness of the times was 
significant of the coming dawn. 

The first era of Scholasticism was the adoption 
of Logic as the form and vehicle for Religion, and 
thus far they were in the right path. 

The -second phase was the attempt to unite Religion 
21* 



246 logic. 

and Philosophy, and this produced new champions of 
Realism. 

The third phase was an opposition : Religion and 
Philosophy were rudely dissevered, and this produced 
Nominalism. 

If, now, we separately consider these three phases 
of the Scholastic philosophy, we shall perceive that 
the first was the just and true one, and that the suc- 
ceeding ones were learning which had to be unlearned. 

That part of the Greek system which could be 
made the form and vehicle of religion, as it is of all 
correct reasoning, was only the Logic. To apply that 
to the service of Faith, was just the first design of 
Christianity towards Logic, and thus far the School- 
men were right ; indeed, it would seem ignorantly 
right ; for while using the forms which constitute Lo- 
gic, they still persisted in calling many other parts of 
the Greek philosophy by the name of Logic, and 
thus making Logic bear the blame which truly be- 
longed to the errors, obscurities, and absurdities of 
exploded systems of metaphysics, theology, and 
morals. 

This is apparent in the works of Alcuin, the con- 
temporary and friend of Charlemagne, and especially 
in his dialogues on " Grammar, Rhetoric, and Logic." 

So, too, Erigena lays down the logical rules of Divi- 
sion, Definition, Analysis, and Demonstration, and 
asserts, that by the use of these man may attain to 



LOGIC OF CHRISTIANITY. 247 

truth, manifestly begging the question, and asserting 
that man attains to truth by arriving at truth. There 
must have been a great superiority of intellect about 
this man, however, as we know that he was regarded 
by the Church as dangerous, and his works afterwards 
placed in the « Index Expurgatorius." More lofty 
was the simple distinction of St. Anselm, that there 
are but two modes of Cognition — Faith and Science ; 
and grander yet the idea, « that Science begins where 
Faith ends," — in the bosom of God ! 

But let us consider the second and third phases. 

Nominalism and Realism were but the reproduction 
in the ninth century of the old Platonian controversy, 
already referred to. Nominal and real were the abstrac- 
tions of what we call respectively universal and par- 
ticular. 

When I speak of a single man, and point him out, 
I designate a real existent individual ; when I speak 
of man, as a common term, is there a real entity cor- 
responding to the word ? The realists said Yes ! the 
nominalists said No ! it is but a name to indicate num- 
bers. This had been the origin of the controversy. 

Plato, with his divine but vague philosophy, had 
asserted that there was a real existence,, an archetype 
in the bosom of God corresponding to the name of a 
class, as man, angel ; Aristotle, that they were only 
generalized names from many individual abstractions. 
And thus these great parents of Logical Philosophy 



248 logic. 

set the example of wrangling to their myriad children 
of the schools. It is curious to see how such a dis- 
pute first connected itself with religion. It was thus : 
the question seemed to involve another and a more 
important one, viz. : " what is the foundation of 
human knowledge ?" Roscellinus of Compeigne, who 
lived in the eleventh century, was the originator of 
the new controversy in the Middle Ages between the 
realists and the nominalists. He was a fierce nomi- 
nalist, and as this led to supposed heresies, he was an 
object of persecution on this account. As warmly 
was the cause of realism espoused by William of 
Champeaux ; and throughout the schools there was a 
word-war of great fierceness on this subject. 

Passing over the quarrels of the schoolmen until 
we reach the time of Roger Bacon, and thus neglect- 
ing many great names in the history of Logical Philo- 
sophy, we are struck with the power of his experiments 
and analysis, and the manifest fact that he deserves 
the name of the founder of Inductive Philosophy ; that 
his " Opus Majus" may justly be considered the 
precursor of the " Novum Organum" of his more 
illustrious namesake, Francis Bacon. 

Disgusted with the categories of Aristotle as tram- 
melling an ardent physical scholar, who must establish 
categories for himself by experience, he considers 
experiment, based upon constant observation, the only 
rule for philosophy, and in his works in the labora- 



LOGIC OF CHRISTIANITY. 249 

tory and with his pen we discern the first dawning of 
the day of Induction. 

For awhile, as was very natural, formal Logic fell 
into disrepute, and gave way to experiment in physics ; 
and from that day down to our own times, there has 
been but little appreciation or understanding of the 
art of reasoning, although it has been constantly used, 
and constantly ignored. Like savages, who breathe 
the invisible air around them and are not aware of 
its existence, so minds of all kinds and calibres have 
used the Logic which they found established as the 
vehicle of thought, without knowing where to make 
their acknowledgments. 

At length the Logic of Aristotle received a shock 
ruder than any which it had yet experienced. 

Long used by the powerful Church, and long 
subtly applied to many sophistries by that Church ; 
it had been accused also of becoming corrupt ; errors 
and crimes, not its own, were imputed to it ; it was 
contaminated by the theology, stained by the prac- 
tices, monopolized by the avarice of the Church ; and 
was conseqently to go through two distinct phases ; 
first, to be punished with that Church ; — and, secondly, 
to be disenthralled and separated from it, The first 
took place at the Reformation, of which premonitory 
symptoms had been seen by Roger Bacon in England, 
in the loth century, and distinct signs by Wiclif in 
the 14th. In this, both Bacon and Wiclif were effi- 



250 LOGIC. 

cient instruments. Still, the battle cries were, nomi- 
nalism and realism. Realism suited the blind belief 
of the Church, and nominalism the unmasking dog- 
matism of the reformers. 

Peter Ramus, in the early part of the 16th cen- 
tury, having published a thesis, controverting some 
of the chief tenets of Aristotle, and disparaging his 
entire system, which system it will be remembered 
had been adopted by the Church, the Pope condemned 
him and his book as " rash, impudent and ignorant ;" 
whereupon Boileau put forth a satire in the form of 
an humble petition, craving " an interdict against 
Reason and Experience, because they would not 
submit to the laws of Aristotle." This satire and 
ridicule gained the day; and when the shock came 
paralyzing the Church, there were weightier questions 
of concernment than those of the schools. It is a 
most interesting inquiry to examine the logical views 
of the Reformers. As a matter of course, they con- 
demned in the most sweeping manner, the logical 
system of Aristotle, endorsed by the Church, and all 
" scholastic dialectics." Perhaps the views of Luther 
are the fairest illustration of their system, if it may 
so be called; and Luther was not ignorant of Logic, 
that being one of his branches when a professor. 
But in a fervour of enthusiasm, he seems to ignore 
rather than disprove the doctrines of Aristotlfe and 
the schoolmen ; asserting with a certain unanswerable 



LOGIC OF CHRISTIANITY. 251 

air: — " In divine things, the Father is the Grammar, 
for he imparts words ; the Son is Logic, and suggests 
order, arrangement and sequence of ideas ; the Holy 
Grhost is Rhetoric, who persuades and presses home." 

And so charging the schoolmen "with having given 
up the substance for silly trifles, he goes on to say 
that, " the Decalogue is the doctrine of doctrines ; the 
Creed the history of histories ; the Lord's Prayer the 
prayer of prayers ; and the Sacrament the ceremonies 
of ceremonies." In short, his purpose, and that of the 
other Reformers, seems to have been to find every- 
thing in the Bible, and to seek for nothing out of it. 
This is not to be wondered at ; it was the period of 
enlightenment ; first, the dark places must be illu- 
minated, before the errors could be made manifest ; 
and the Reformers were right in their views for the 
times and to effect the purpose desired. 

The light which was thus produced, soon began to 
shine with great power and brilliancy, and its effects 
were no less to be observed in philosophy than in 
religion and morals. The kingdom of Nature lay 
exposed to its searching beams, and invited the 
Naturalist to examine and comprehend her works ; 
the Mind, disenthralled and opened, was no less a 
subject of most interesting study; the reformation in 
religion was but the precursor of the birth of Experi- 
mental Philosophy, and the Reformers were heralds of 
Lord Bacon as its interpreter. 



252 logic. 

(57.) The Logic of Experimental Philosophy. 

In order clearly to understand the origin of Ex- 
perimental Philosophy, we must remember that the 
union of Christianity and philosophy had been fairly 
tried and had proved unsuccessful ; scholasticism, 
fulfilling its true purpose, but not that designed by 
its founders, in gradually emancipating man's reason 
from the thraldom of the schools of theology, by 
manifesting its own imbecility, had failed in its first 
design, that of intellectual progress. Now, an ele- 
ment seems to have been introduced into philosophy, 
which till then had been considered unimportant ; 
and that was observation and experiment ; or, to use 
the term by which we have expressed the methodical 
and successive observations of such phenomena in 
nature as will lead us to general laws, — Induction. 
Aristotle himself had stated the value of induction 
for the discovery of new truth ; and men, in all ages, 
had used it as an exercise of common sense in their 
ordinary conduct ; so that it must not be supposed 
that in any sense, Bacon is its inventor. He only 
applied it by system to natural science. 

Logic, which is the vehicle of truth in its intellec- 
tual passage from premiss to conclusion, had only 
reasoned upon the Tcnoivn and conceded: — mainly 
from some general law to a particular example ; now 
its premisses were to be new truths aggregated by 



LOGIC OF EXPERIMENTAL PHILOSOPHY. 253 

experiment ; it was to reason from many particular 
examples to the establishment of a general law. 
This, then, let it be borne in mind, was the only new 
duty which Logic was called upon to perform ; and 
this, had it been desired, she had always been ready 
and able to do. 

She had been the fearful servant of ecclesiastical 
authority and theocratic reverence ; to argue without 
permission of the Church, or otherwise than by 
priestly dictation, was worse than vicious ; it was 
heretical. 

But when the reformation in Europe had thrown 
contempt on the authority of the Church, the intel- 
lectual bonds of Europe also were burst, and the 
childhood of experimental philosophy began. The 
unchangeable principle of reasoning was simply 
applied to new subjects and investigations. 

There were two great realms to be emancipated, or 
rather released from prison and darkness : the realms 
of Nature and Thought, or as they are ordinarily 
called, matter and mind. The founders of the new 
system adopted the same method for both, Analysis : 
constant experiment and observation upon the pheno- 
mena of the outer world, and upon those of the con- 
sciousness within. 

Bacon was the early interpreter of Nature ; Des- 
cartes the analyzer of Thought. To each is due an 

illustrious share of the developments in philosophy. 
22 



254 logic. 

But Bacon is the more distinguished, because his in- 
vestigations were made in every domain of nature ; 
and his system is at once more intelligible and popular 
on that account. 

The starting point of Bacon's philosophy was the 
assertion that the universe is a great store-house of 
facts; and that it is man's duty and interest, and it 
ought to be his pleasure, to explore, discover and 
understand these facts, not only in their isolated cha- 
racters, but in their relations to each other and to the 
universe itself. His experiments and his use of the 
experiments of others, was to enable him to arrive at 
general laws of the universe. Now, corresponding 
with the world around us, that is, the world of Nature, 
there is a world within us, — the world of Thought. 
Let either be impaired or cease to -exist, and in just 
such a proportion is the other impaired or does it 
cease to exist. 

To unite them we have sensation and perception, 
and the union is lost if sensation and perception fail. 

The happy union, then, of Thought and Nature 
would lead man to Truth, and to attain to Truth is 
his highest aim. It will at once be seen that this 
was the establishment, not of a logical, but of a 
philosophical system. But to proceed : the various 
forms which truth assumes to inspire the faculties and 
entice the pursuits of men, are called sciences, and 
by an examination of multitudes of these phenomenal 



LOGIC OF EXPEEIMENTAL PHILOSOPHY. 255 

facts, the true definitions of the sciences might be 
made, their true relation determined, and a plan of 
classification formed for practical purposes. 

Such then, very briefly, was the aim of the new 
experimental philosophy, a great restoration which was 
proposed by Bacon in his Instauratio Magna. With 
it directly, Logic had but little to do ; but that little 
led men of science into errors, which remain to the 
present day. 

Without attempting to enter into the details of the 
" Great Restoration," it will be well to consider some 
of the steps proposed by Bacon, as preliminary to it. 
Finding, in his inquiries about facts, or phenomena, 
that they greatly differ in importance ; that some 
are simple, others complex ; some are easy of inter- 
pretation, others very difficult ; he proposed a classi- 
cation of the instances in which any phenomenon or 
fact occurred, and this should be a sort of value scale 
of the instances in which a special phenomenon 
occurred. These he calls prerogative instances, or 
those cases of most importance to us in interpreting 
a fact or a series of facts. He has stated twenty- 
seven of these, from which we shall choose four, 
as better illustrating their own meaning than it can 
be done in other words. Our purpose is not to use 
these, but merely to indicate their nature and design. 

I. Solitary instances, or those in which two or 
more objects agree or differ in all qualities save one. 



256 logic. 

II. Forth-showing instances. Under this head, 
range those facts or instruments which show forth the 
quality in question in the highest degree ; as a gal- 
vanic battery, in electricity, and a barometer in pneu- 
matics. 

III. Analogous instances. Those in which are found 
objects bearing a resemblance of purpose or relation, 
however unlike the objects themselves may be. Thus, 
a camera obscura is analogous to the eye, and a sys- 
tem of waterworks to the heart. 

IV. Crucial instances. There are two probable mean- 
ings to the word crucial, as here used. It may be 
the putting nature to the torture — crucifying her — to 
wring from her her secrets, or it may have reference 
to the way-side crosses, which at the parting of the 
roads indicate the true direction to the traveller. 
Franklin's electric kite might be called a crucial in- 
stance, in the first sense. Such also, in the second, 
was Newton's law of gravitation, a finger-board for 
ever to point to the true direction of investigation 
and belief, concerning our solar system. 

The other instances, which we cannot stop to men- 
tion, are designed to exhaust the classification of 
experiments on facts, and to lead to induction ; and 
here began the danger and difficulty : it was here 9 
also, that the syllogism, which Bacon despised and 
misunderstood, was, and always is, the only safe guide 
of Philosophy. For, suppose the facts ranging under 



LOGIC OF EXPERIMENTAL PHILOSOPHY. 257 

these instances to be established, how many of them 
will give us the right to the establishment of a general 
law, or a distinct science ? We have seen that, in 
most sciences, we only attain to likelihood. On ac- 
count of human ignorance, the process has been this: 
— we first establish a few facts : we then adopt a hypo- 
thesis or theory based upon them, i. e., jump at the 
general law, simply in order to make a ?iidus for our 
accumulating facts ; and thus proceed to verify — if 
the new facts will verify — our proposed theory. The 
tendency of man's mind is so great, however, to repose 
upon a darling theory, even if it be unsound, and 
rather to seek- — like an advocate — for such facts and 
statements as will support it, than to look for just 
proof, and in the absence of such to discard it, — that 
induction has often led to grievous error. Many a 
student has learned one theory of some part of Na- 
tural Science, and when he had just mastered it, has 
been obliged to discard it for another. 

In the consideration of Judgment, Bacon has given 
special attention to the Fallacies which assail the 
mind of man. These he calls idols of the intellect, 
and in almost every case, since they are contained in 
false judgments, they belong to the class of material 
fallacies. But all these idols occasionally assume the 
garb of logical fallacies. 

These idols, or stB^a, which Bacon calls "the deepest 

fallacies of the human mind," are the sources of error 
22* R 



258 logic. 

which assail men in their investigations in Philosophy, 
and which "must be renounced, and the intellect 
wholly freed and purified therefrom," before we can 
hope for healthful progress. By the word idol, 
Bacon means the prejudice which stands in our way 
of receiving truth, and the bias of the mind from 
which such prejudices arise. 

But these idola will most clearly explain them- 
selves : they are of four classes. Idola Tribus, Idola 
Specus, Idola Fori, Idola Theatri ; and with reference 
to these, an author of his own time remarks : " The 
temple which he purified was not that of nature it- 
self, but the temple of the Mind; in its innermost 
sanctuary were all the idols which he overthrew." 

1. The idols of the Tribe are those which are im- 
posed upon the understanding by the general nature 
of mankind : in other words, they belong to the human 
tribe, in its universal comprehension. Thus, he asserts 
that men — as men — are quicker to be moved by affirm- 
ative and active events than by negative and privative, 
though in justice they should be moved by both. To 
illustrate this, he tells the story of the Greek, who 
was shown, in Neptune's temple, the votive pictures 
of those who had escaped shipwreck, and when asked 
if he did not now acknowledge his divinity, said, — 
" show me first where those are painted who paid their 
vows and were then shipwrecked." 

2. The idols of the den or cave spring from the nature 



LOGIC OF EXPERIMENTAL PHILOSOPHY. 259 

of each particular man, and grow out of his peculiar 
nature both of mind and body ; — these may also be 
fostered or developed by education, custom or acci- 
dent. The name is suggested by fancying the con- 
fusion and error of a man being brought out of a 
dark den or cave into the full light and glory of 
Nature. This finds its counterpart in the world of 
philosophy, where men only emerge from the den of 
their minds to find confusion and disorder in the 
beautiful universe of God. 

3. The idols of the market are errors which grow 
out of words and communication, such as are the 
pass-words and common coin of conversation and 
intercourse in the market-place ; and they imply, like 
the idols of the tribe, a social organization, but on a 
much more limited scale. Instead of being universal 
with men, they are errors which belong to a small 
circle, like a crowd in a market-place, moved at the 
sound of an orator's words, by a common impulsion 
of prejudice, passion or other emotion. These idols 
are causes of the greatest disturbance, as they are 
immediately connected with the naming of things, 
" for words are generally given according to vulgar 
conception, and divide things by such differences as 
the common people are capable of; but when a more 
acute understanding or a more careful observation 
would distinguish things, better words murmur 
against it." 



260 LOGIC. 

Thus, many words in our every day use convey no 
definite meaning to the mind ; but have, in their very 
indefiniteness, so many shades of meaning that they 
are a constant cause of verbal fallacy. As special 
reference has been made to such words in the chapter 
on Fallacies (X.), it will only be necessary to mention 
a few such to illustrate the idols of the market-place: 
such is the word republic, which we have been apt to 
confound with democracy ; Liberty means either free- 
dom or license, as its champions wish — and taste and 
beauty have as many forms as there are eyes to see 
or imaginations to indulge. 

The last of the sources of error enumerated among 
the idols of Bacon, are the idols of the theatre. 
These he distinguishes from the others, as perhaps of 
more social power and influence. Of these, he says, 
" they are superinduced by false theories or philoso- 
phies, and the perverted laws of demonstration." 
They are comprehended under three heads : — Parti- 
sanship, Fashion and Authority. 

Partisanship is the generic name under which are 
found factions in politics and in religion — and under 
whose influence wars of creed and caste have so often 
desolated the world. 

Fashion is a kind of partisanship, which, however, 
has few opponents, and no great rivalries ; but which 
pervades society from high to low. We do not refer 
to its simple sway in dress, equipage and social life ■ 



LOGIC OF EXPERIMENTAL PHILOSOPHY. 261 

but to its more comprehensive dominion, over all the 
works and thoughts of man, over art, science, reli- 
gion. Great masses of men are herded like cattle, 
and driven willingly in the train of this all-swaying 
Fashion ; resting their happiness here, and their hopes 
in an eternal future, upon the dictum of Fashion. 

As Fashion partakes of the nature of Partisanship, 
so is Authority strengthened by an alliance with 
both. This consists in blind obedience to an existing 
control, and reliance upon it, without the use of our 
own judgment. 

As God, who has given man Reason, has made 
some things higher than that reason, but nothing 
repugnant to it, every theory of authority in Church, 
in state, or in general philosophy is, of right, to be 
examined by our reason, before we can accord to it 
our belief. Reliance upon authority, without a due 
understanding of its claims, is to treat our own moral 
constitution with injustice, and to stop the wheels of 
healthful progress, both of individuals and societies. 

It was an increasing distrust of authority that 
brought about the Reformation in the Church ; that 
exploded the scholastic philosophy and the supersti- 
tious practices of the Middle Ages ; and that destroyed 
the divine right of kings, with a host of evils which 
appertained to it. To examine the claims of asserted 
authority is to investigate nature and mind — and to 



262 logic. 

do this, is to move forward to new and glorious vic- 
tories in the domains of both. 

In reviewing these error-sources, it is scarcely 
necessary to remark that it is the abuse and not the 
use of our words and associations which lead to them. 

Thus, the idols of the tribe, would not be false and 
deceitful, if man should concur universally and every- 
where in just and truthful opinions ; nor would the 
den darken men's minds to the true light, if they 
were capable of carrying into their meditation the 
true elements of combination and just views of the 
objects in the universe around them. Heraclitus has 
told us « that men seek the sciences in their own 
narrow worlds, and not in the wide one." Such is 
the influence, but not the necessary consequence of 
the den. 

So it is easy to avoid the errors which grow out of 
ambiguous words, such as those which mark the idols 
of the market; by demanding just definitions, and 
when such cannot be given, either agreeing for argu- 
ment sake upon one which is not just ; or, declining 
to argue at all where the very question is involved in 
obscurity. 

We may observe, concerning the idols of the 
theatre, that partisanship has its good as well as its 
evil character ; and that to championize the right is 
noble and just ; it is, however, even in such a cause 
that its tendency is to extremes. 



LOGIC OF EXPERIMENTAL PHILOSOPHY. 263 

So fashion, crowds of whose votaries are miserable 
and self-tortured, is incident to man's social character, 
and is productive to those who use it aright, of method 
and comfort, and success. Although fashion has 
done much evil, it could not be spared in our social 
or intellectual systems. Nor must Authority, how- 
ever formidable the name, be accounted of slight 
importance ; for under just authority are ranged 
obedience, order and wholesome discipline ; without it 
government would be anarchy, and education would 
be a curse instead of a blessing. It is the time- 
honoured abuse of it, which demands our dislike and 
resistance. 

Beyond a few, and very erroneous allusions to the 
Logic of Aristotle, Bacon and his immediate succes- 
sors did very little for it as a science. 

Hobbes seems to have had just views of the syllo- 
gism, as "the instrument of demonstration," but 
carried his investigations — his written ones at least — 
very little beyond such a statement. 

Resting upon the basis of the Baconian philosophy, 
the thinkers of the seventeenth and eighteenth cen- 
turies seem to have neglected the art of reasoning for 
the subject-matter about which we reason, and thus to 
have entirely confounded Logic with the art of think- 
ing. For this they had the authority of their great 
master, Bacon, who, in his " Advancement of Learn- 
ing," has divided the Art of Judgment into Induction 



264 logic 

and the Syllogism ; and has classified as four kinds of 
demonstration : 1. That by immediate consent and 
common notions ; 2. By Induction ; 3. By Syllogism ; 
and 4. By Congruity. The error of this classification 
is at once apparent to us. 

Indeed it may justly be said, that in everything 
pertaining to Logic, in its proper meaning, Lord Bacon 
is entirely at fault ; while in everything which bears 
upon Experimental Philosophy, he is great beyond 
any competitors ; he is the inventor of Induction, 
and as a few words have shown that all induction 
must be brought to the syllogism to verify and test 
the laws at which we arrive, his philosophy can be 
easily disconnected from his Logic, and the faults of 
the latter exert no evil influence over the excellencies 
of the former. 

Many logicians in England, France and Germany, 
followed in the steps of Bacon in the seventeenth 
century, attempting to unite Logic and Experimental 
Philosophy in a manner which was injurious to the 
former. 

Locke, misunderstanding the syllogism as Lord 
Bacon had done, discards it from his system, and 
bases his views of the understanding on two sources 
by which ideas enter the mind, viz. : Sensation and 
Reflection. But to show how so great a thinker 
erred, by his false notions of the syllogism, he states 
reasoning to consist of four parts : — 1st. Finding 



LOGIG OF EXPERIMENTAL PHILOSOPHY. 265 

proofs ; 2d. Arranging them ; 3d. Showing their con- 
nexion ; and 4th. Employing them correctly. 

Now, what is all this, but, 1st. Finding middle 
terms by which to establish premisses ; 2d. Stating 
syllogisms; and 4th. Combining arguments. As for 
the 3d, that is included in the 2d, for they cannot be 
arranged without their connexion being manifest. 

Leibnitz, in Germany, seems to have thrown light 
upon the theories of Descartes, and to have elucidated 
also many things in Locke. 

Milton has been called the most learned man of his 
age ; he vindicated this opinion by writing upon 
almost every subject within the range of knowledge, 
and in most cases, writing well. We are not, there- 
fore, astonished to find that he has written a work on 
Logic. It is in Latin, and seems to be very little 
known. In that he adheres to much of the Aristote- 
lian doctrine, and specially championizes Peter 
Ramus, the logical Martyr. He divides Logic, which 
he calls the chief of Arts, into two kinds — Natural, 
i. e., the faculty of reason in the human mind ; and 
Artificial, i. e., rules for directing the operations of 
that faculty. But even Milton erred in stating that 
"it belongs to Logic to lead us from universals to 
particulars," which would limit the Syllogism to 
Deductive reasoning. 

In this state of confusion, Logic existed until the 
new rise of Philosophy in the 18th century, the 

23 



266 logic. 

source of which was the continent of Europe rather 
than England. 



(58.) Logic in the Eighteenth and Nineteenth 
Centuries. 

But little remains to be said, in order to complete 
this brief sketch of the History of Logic. Even to 
mention the names of the principal writers who have 
sprung up under the impulse of the Baconian philo- 
sophy, from that time to the present, would occupy 
more space than we can give; and to discuss their 
metaphysical works would in this connexion be diffi- 
cult and improbable. 

The logicians of the eighteenth century seem to 
have bent their energies to the task of classifying the 
science; of making such a logical arrangement as 
would make much labour unnecessary, and find for 
each its true niche in the temple of Truth. 

In England, Doctor Isaac Watts published a trea- 
tise on "Logic, or Right Use of the Reason," which 
is a compound of Logic and Philosophy alike injurious 
to both. Selecting a few tenets from Aristotle, from 
Lord Bacon, and from the Schoolmen, he has endea- 
voured to harmonize them. In another of his volumes, 
" The Improvement of the Mind," he has moved upon 
surer ground and with much better success. 

Bishop Berkeley wrote the » Principles of Human 



EIGHTEENTH AND NINETEENTH CENTURIES. 267 

Knowledge," a work of profound thought and excel- 
lent reasoning ; and Bishop Butler has exemplified 
the correct use and application of Logic, in his famous 
treatise on the " Analogy of Religion." 

France has also produced in the eighteenth century 
many fine logical minds, who have devoted themselves 
to science specially in attempts at classification ; 
among these were D'Alembert, Diderot, and their 
coadjutors, known as the Encyclopaedists, who, in the 
eighteenth century, startled the world not less by 
their methodical arrangement of the sciences, than 
by the scepticism which their studies induced, and 
the atheism or denial of God's existence, which took 
the place of doubt. 

It would be improper in a treatise of this kind to 
do more than simply refer to the present writers on 
Logic, and the present condition of the science. 

Archbishop Whately has renewed the Logic of 
Aristotle in its pristine vigour ; and placed it in its 
true position as the only sure guide or Art of Reason- 
ing. Many English writers have differed from him ; 
some, in his conception of the meaning and scope of 
Logic itself, and others as to the extent to which the 
Aristotelian system may be carried. 

Of the first, may be mentioned Mr. J. S. Mill, 
whose work, according to the view we have taken, 
may fitlier be called " an encyclopaedia of philosophic 



268 logic. 

tenets connected with, or resulting from, the Science 
of Logic." * 

Of the second, are Sir William Hamilton, and 
Mr. Augustus de Morgan, who "would develop more 
ih^nfour categorical propositions, and establish what 
we have called the "New Analytic." 

The most important changes, however, in the ap- 
plications of Logic to science are to be found, as has 
been said, in the subject of Categories and Classifica- 
tion ; and to this, in illustration of the later move- 
ments of the science, we shall now give a few words. 
It will be at once perceived, that the object is to 
reach a summum genus under which all the sciences 
may range, and then by a logical tree of division, to 
place all the lower classes and their co-ordinate 
species, in their proper places. In any less general 
classification it is evident that the principle of classi- 
fication will be changed for the different sciences. 

(59.) Of Categories and Classification. 

This is a part of the duty of Method. 

The Categories of Aristotle which have already 
been explained, may be considered the basis of the 
classification of the sciences. For although there 
has been, in former times, much dispute concerning 

* Neil's Art of Reasoning, p. 234. 



OF CATEGORIES AND CLASSIFICATION. 269 

their true reference, that is, whether it be to words, 
or things, or conceptions, it is now allowed that, 
imperfect as they are, they are designed to apply to 
the summa geneva, under which all things which arc 
named may range themselves. This establishment of 
proper summa genera, then, is the true start point of 
classification. 

Many writers have simplified these categories mainly 
by reducing the number. The schools of Pythagoras, 
Plato, and Epictetus had each its corresponding list 
or table ; Locke wrote three, viz. : Pliysica, Praetica 
and Semeiotica, or, as they have been translated, 
Substance, Modes and Relations ; Hume, two, viz. : 
Ideas and Impressions. But these are manifestly 
none of them, of that practical form and character 
which is desirable for useful reference, and hence it 
has been the aim of later writers, especially upon 
Metaphysics and Logic, to write out tables of classi- 
fication which should comprise and methodize all 
forms of human science. To classify palpable, tan- 
gible objects, is to arrange them in groups according 
to a certain method, and that method will usually be 
based first upon the great division of kingdoms, and 
afterwards upon the relation of species to genus. 

If we reflect for a moment upon the innumerable 
forms of life and existence in the three great king- 
doms, iinimal, Vegetable, and Mineral, we shall at 

once be struck with the difficulty and labour of a just 
23* 



270 LOGIC. 

and adequate classification ; and yet, strange as it may 
seem, true progress in any of these branches has but 
kept pace with such a classification ; the naming and 
placing of a minute species in its proper place being 
the necessary way of fixing it there for ever. 

It has already been said that the basis of physical 
classification is the establishment of the summum ge- 
nus, and that the rules of Logical division must deter- 
mine all the subaltern genera and species. This must 
serve us for the classification of the known and deter- 
mined ; but in the world of Theory, another mode may 
with propriety be adopted : it is the classification by 
series, investigated by Comte. It consists in select- 
ing some particular phenomenon, the laws of which are 
to be investigated, and then ranging the various ob- 
jects which sustain a relation to it, in a nearness pro- 
portional to that relation. 

With this subject of classification, scientific nomen- 
clature is immediately connected, and it will appear 
how important this must be regarded, when we con- 
sider that the value of the classification will depend 
upon the names of the different classes, as to their 
precision or total want of ambiguity, their complete- 
ness, or expressing the whole of the class specified, and 
their expressiveness, in denoting the properties of the 
object, and the reason of its classification. Thus, in 
chemistry, a law of nomenclature has been formed, 
based, indeed, upon some unfortunate beginnings, 



OF CATEGORIES AND CLASSIFICATION. 271 

which have been allowed to remain, but very system- 
atic, and universal in its reception. 

But the high aim of metaphysical philosophers, to 
smooth the paths of Logic, has been, not the classi- 
fication of one science, but the analysis and classifi- 
cation of universal Science, the establishment of a 
complete table, in which all human investigation 
should find its place, and link itself to the great mind 
of all ages in its study of all topics within its sensual 
or intellectual range. 

It will not be attempted to give a history of classi- 
fication, nor to prepare or copy a complete table of 
any previous author, but rather to indicate the manner 
in which it has been done, with a general reflection 
upon the results attained. Classification, to be logi- 
cal and just, must be made after certain investigations, 
which are necessary to determine the true class of 
the object m question. This will be done in Physics 
by formal analysis, such as the organic analysis in 
chemistry, and in the exact sciences by the applica- 
tion of the principles of demonstrative proof. 

Passing by, only because our limits do not permit 
their consideration, the system of Bacon, which was 
adopted by the French Encyclopaedists of the last 
century as the basis of their great work, " L'Ency- 
clope"die Methodique," and the details of the system 
of Locke, we come down to our own times before we 
find any definite attempt to supply the want. An 



979 



LOGIC. 



eminent Scotch writer, as he reviewed the efforts of 
previous philosophers to classify human knowledge, 
asserted that it was an impossible task, and so, from 
its magnitude, it would fairly seem. 

Nothing daunted by such an assertion, Coleridge 
suggested the plan of classification, which was adopted 
in the arrangement of the English " Encyclopaedia 
Metropolitana," but which he found to require, after 
he had exhausted his categories, an additional cate- 
gory of "Miscellaneous" species; the unfortunate 
subalterns which had no summum genus under which 
to range themselves. 

Among the curious but highly philosophic remains 
of Jeremy Bentham, is a proposed system of scientific 
classification ; but, like his other works, it is only a 
store-house of theory from which less gifted but more 
practical men draw capital for constant use. 

All the more modern writers agree in considering 
the system of Ampere the most correct and useful. 
It is based upon the two categories of mind and 
matter, and under these it expands into a very great 
number of subordinate sciences, many of which, it 
must be said, are created, i. e., in name to fill up 
gaps which would spoil the symmetry of his table. 

It is not our purpose to write out his table in full ; 
it would be out of place in a text book, as it could 
only be examined, not studied ; but we will form a 



OF CATEGORIES AND CLASSIFICATION. 273 

tree of one or two of his subjects, to illustrate his 
plan, and indicate its truthfulness and use. 
His First Table contains : — 

(Kingdoms). 
f Cosine-logical sciences, ^j C Noological sciences, "j 

[ i. e., pertaining to matter. J I i. e. } pertaining to mind, j 



Cosmologies proper. Physiologies. Noologics Social sciences. 

I | proper. | 



Mathematics. Physics. Nat. sciences. Med. sciences. Philosophies, &c. Ethnology, 

I | | | - &c. 

Geometry, &c. &c. &c. &c. i 

| &c. 

Elementary geometry, &c. 

I 
Synthetical and analytical geometry, 
&c. 

Of these there are several tables and more than a 
hundred branches. In thus indicating rather than 
writing out in full the tables of Ampere, we spare 
the student the reading, in place, of many names 
unknown to our ordinary scientific studies, such as 
Dialegmatics — Eleutherotechnics — Technesthetics, 
while we present to him what is alone our present 
purpose, the theory and principle of classification. 

The chief merit of his tables, which he spent his 
life in constructing, seems to be that there are no 
cross divisions — that no subordinate science lies out 
of its own class or laps over into another — errors 
which rendered Bacon's system worthless, and which 
caused Bentham to abandon his great idea and leave 
it in its inchoate form. 

Auguste Comte, who has given to the world, in his 

S 



274 logic. 

Cours de la Philosophic Positive, his views of philo- 
sophy, did not attempt so much to classify science as 
to determine the true relation between general science 
and positive science : to make positive science more 
general in its application, and general science more 
practical and positive. This has been his life-work. 
There is much of his work which bears indirectly 
but dangerously upon religious belief, and there is 
an elaborate description of the historical progress of 
positive science — through what he calls the mystical 
and metaphysical eras, to the positive. 

To explain more clearly his view of this 'positive 
era, it is that in which the mysticism or mythology of 
ancient and early times, as well as the crude meta- 
physical notions of the Middle Ages, which found their 
issue in astrology and magic, are swept away, by the 
light of modern free thought and investigation, and 
in their place are substituted the laws of creation, laws 
which regulate its origin, its progress and its destiny. 
There are six positive sciences, which include every 
thing that can be known. These are Mathematics, 
Astronomy, Physics, Chemistry, Biology, and Soci- 
ology. 

But it is not within our scope to explain his philo- 
sophy ; we have only to do with its Logic, and this 
is found in his classification. 

The subject of classification is yet open, and will 
become, without doubt, clearer and more practical as 



OF CATEGORIES AND CLASSIFICATION. 275 

science advances to the discovery of the proximate 
laws of creation. 

(60.) Conclusion. 

From the foregoing investigation of the art of Rea- 
soning, we may pause a moment at the end to reflect 
upon its real value and importance. If Logic is really 
the art which controls and guides the reason in its 
workings, and without which we can attain to no truth 
upon which the reason is exercised, it is surely worthy 
of a high place in the catalogue of elementary studies, 
and the statement and adoption of its laws must be 
considered of the first importance. 

And, above all, should it be placed upon its own 
foundation, and dissociated from any other sciences 
which either rob it of its own identity, or use it with- 
out acknowledging its office. 



APPENDIX. 

EXAMPLES FOR PRAXIS. 

Logical praxis consists in the application of the 
rules of Logic as a test of all the forms of argument. 
The following examples for praxis are designed to give 
ease and logical quickness of detection to the student. 
They comprise illustrations of all kinds and forms 
of argument : — regular syllogisms ; irregular and in- 
verted arguments ; compound arguments ; fallacies of 
every kind ; curious propositions ; examples of the 
processes of generalization and division ; amphibolous 
sentences, &c, &c. A certain number of these should 
be given to the student as an exercise with each lesson, 
upon the review of the subject. He should be re- 
quired to state what each is in its present form ; if a 
fallacy >, of what kind ; if a logical fallacy, to write it 
out by symbols, and thus to expose its invalidity ; if 
an inverted argument, to put it in the true order of 
sequence of premiss and conclusion ; if an enthymeme, 
to supply the suppressed premiss ; if in an imperfect 
mood, to reduce it to one of the perfect moods of the 
first figure ; in a word, to show by this practice the 

(277) 



278 APPENDIX. 

truth of the assertion made at the beginning of this 
book, and steadily kept in view throughout the work, 
that every valid argument, whatever its form, may 
be brought directly to the dictum of Aristotle as the 
final test of argument. 

In a few of the more difficult examples, to guide 
the student, a reference has been made to the page 
on which their type may be found. Some selected 
arguments from the Latin authors, generally read in 
the schools, have been added, as of interest to the 
classical student. 



1. Jupiter, Saturn, Venus, Earth, &c, move round 
the sun in ellipses ; these are all planets ; therefore 
all planets move round the sun in ellipses. 

2. Induction is the only true science of reasoning; 
Syllogistic Logic is not induction; therefore Syllo- 
gistic Logic is not a true science of reasoning. 

3. No one is good who commits sin ; all men 
commit sin ; therefore there is none good except 
God. 

4. A story is not to be believed, the reporters of 
which give contradictory accounts of it; the story 
of Napoleon's life is of this kind ; therefore it is not 
to be believed. 

5. Every one desires happiness ; virtue is happi- 
ness ; therefore every one desires virtue. 



EXAMPLES FOE LOGICAL PRAXIS. 279 

6. No evil should be allowed that good may result ; 
all punishment is an evil ; therefore no punishment 
should be allowed. 

7. Those who are over-credulous should not be 
believed ; the ancient historians were over-credulous ; 
therefore we should believe nothing they say. 

8. An American citizen should be free ; I am an 
American citizen ; therefore I should be allowed to 
do whatever I please. 

9. The Duke yet lives that Henry shall depose, 
(v. p. 193.) 

10. All the peaches in this field are worth one 
hundred dollars ; this is one of the peaches in this 
field ; therefore it is worth one hundred dollars. 

11. Ought we to act from expediency as a motive? 

12. Ought not children to obey their parents ? 

13. A designing character is not worthy of trust ; 
therefore I do not trust engravers. 

14. All good men are beloved by their associates : 
this man is beloved by his ; therefore he must be 
good. 

15. Pallas ne exurere classem 

Argivum atque ipsos, potuit submergere ponti. 

* * * * * 

Ast ego que Divum incedo regina Jovisque 
Et soror et conjux, una cum gente tot annos 
Bella gero. (v. p. 157.) 

16. Happiness consists in obedience to the Divine 



280 APPENDIX. 

Laws ; this obedience is virtuous conduct ; virtuous 
conduct is the subordination of the inferior to the 
superior in our nature ; this subordination is induced 
by self-control ; therefore happiness is the result of 
self-control. 

17. Crime is a violation of the laws of our country ; 
piracy is crime ; this man belongs to a band of law- 
less men, and this band has been taken in the very 
deed of piracy ; therefore he has violated the laws 
of his country. 

18. He that is of God heareth my words ; ye there- 
fore hear them not, because ye are not of God. 

19. We must do one of three things — go back, 
stand still, or go forward ; we cannot go back or 
stand still ; therefore we must go forward. 

20. "Ay, in the catalogue ye go for men — 

As hounds and greyhounds, mongrels, spaniels, 

curs, 
Shoughs, water-rugs, and demi-wolves are 

called 
All by the name of Dogs." (v. p. 72.) 

21. All that glitters is not gold; tinsel glitters; 
therefore it is not gold. 

22. Warm countries alone produce wine ; therefore 
Spain produces wine. 

23. Quo melior servo quo liberior sit avarus, 
In triviis fixum, cum se demittit ob assem, 



EXAMPLES FOR LOGICAL PRAXIS. 281 

Non video. Nam qui cupiet, metuet quoque 

porro 
Qui metuens vivit, liber mihi non erit unquam. 
Or, The fearful man is not free : the miser is fear- 
ful ; therefore the miser is not free. Hor. Ep. 1, 16. 
The following strong eulogium of Logic is an argu- 
ment of the schoolmen : — 

24. Utque supra iEthereos sol aureus emicat ignes, 
Sic artes inter prominet hsec Logica ; 

Quid ? Logica superat solem ; sol namque, 

diurno 
Tempore dat lucem, nocte sed hancce negat ; 
At Logicse sidus nunquam occidit ; istud in ipsis 
Tarn tenebris splendet, quam redeunte die. 
Cum hoc, ergo propter hoc, a form of the non causa 
pro causa, is broadly illustrated by the following : — 

25. The encroachment of the sea upon that bank 
upon the coast of Kent, known as the Goodwin Sands, 
rendering it very dangerous to navigation, led to the 
appointment of a committee of parliament to inquire 
into the subject. The committee went down, and 
examined among other witnesses an old man, who, 
when asked what he regarded as the cause of this 
encroachment, replied, after some minutes' thought, 
that he did not know, unless it had something to do 
with Tenterden steeple ; as he remembered nothing 
of the kind before they began to build that steeple ; 
but it had been steadily growing worse ever since. 

24* 



282 APPENDIX. 

26. Horses are stronger than men ; elephants are 
stronger than horses ; therefore elephants are stronger 
than men. 

27. Men need the restraints of government, be- 
cause they have vicious propensities. 

28. Unjust laws endanger the stability of govern- 
ment, because ( ) ; laws which enslave man's 

conscience are unjust, because ( ) ; therefore 

laws which restrain the freedom of conscience endan- 
ger the stability of government. 

29. If we suppose the telegraphic connection from 
London to be made around the world, and the trans- 
mission to be instantaneous, then a message starting 
from London at 12 o'clock to-day would reach Lon- 
don at 12 o'clock yesterday. 

30. If men are to be punished hereafter God must 
be the punisher ; if God be the punisher the punish- 
ment must be just; if the punishment is just the 
punished must be guilty ;. if they are guilty, they 
could have acted otherwise ; if they could have acted 
otherwise, they were free agents ; therefore, if men 
are liable to punishment in another world, they must 
be free agents. 

31. This medicine cured a very difficult case of 
disease ; therefore it will cure every disease. 

32. Among the most bitter persecutions known to 
history were those of the French revolution ; there 
fore they must have been religious persecutions. 



EXAMPLES FOR LOGICAL PRAXIS. 283 

33. Testimony is likely to be false ; the existence 
of the pyramids depends on testimony ; therefore we 
may doubt whether there are pyramids in Egypt. 

34. No man can perform impossibilities; a miracle 
is an impossibility; therefore no man can perform a 
miracle. 

35. With God all things are possible. 

36. No man can do these miracles which thou 
doest, except God be with him. 

37. Si testibus credendum sit contra argumenta, 
sufficit, tantum judicem esse non surdum. — Bacon s 
Antitheta. 

38. Hsec, si displicui, fuerint solatia nobis ; 

Haec fuerint nobis prsemia, si placui. — Mar- 
tial. 

39. From the existence of bad morals springs the 
making of good laws ; from good laws arises the safety 
of the commonwealth; from the safety of the com- 
monwealth, all social good things flow; therefore, from 
the existence of bad morals come all good things to 
society. 

40. Si saperem odissem jure sorores, 
Numina cultori perniciosa suo, 

At nunc (tanta meo comes est insania morbo), 
Saxamemor refer orursas ad ictapedem. — Ovid. 
(v. p. 157). 

41. Caesar oppressit patriam ; Tullius non oppressit 
patriam ; ergo ( ). 



284 APPENDIX. 

42. Una Eurusque ; notusque ruunt, creberque pro- 
cellis, Africus. 

43. For whom he did foreknow, he also did predes- 
tinate to be conformed to the image of his Son ; that 
he might be the first born among many brethren. 
Moreover, whom he did predestinate them he also 
called ; and whom he called them he also justified ; 
and whom he justified them he also glorified. — Rom, 
viii. 29, 30. 

44. When the sun is in Cancer it is summer ; it is 
now summer ; therefore ( ). 

45. All persecution for conscience sake is unpleas- 
ing to God, because it is injustice. 

46. Genius must join with study to make a great 
man ; this man will never be great, for though he has 
genius he cannot study. 

47. No man can serve two masters. Ye cannot 

serve God and mammon. 

48. Pride and innocence are incompatible. The 
angels are innocent, — therefore (- ). 

49. In this life we must either obey our vicious 
inclinations or resist them ; if we obey them we shall 
have sin and sorrow ; if we resist them we shall have 
pain and labor ; therefore we cannot be free from 
trouble in this life. 

50. This doctrine cannot be proved from the Gos- 
pels ; nor from the Acts of the Apostles ; nor from 
Epistles ; nor from the Revelation of St. John ; 



EXAMPLES FOR LOGICAL PRAXIS. 285 

therefore it cannot be proved from the New Testa- 
ment, (v. p. 214-215.) 

51. It is a sin to kill a man ; a murderer is a man ; 
therefore he should not be hanged. 



These examples may be increased at the pleasure 
of the teacher. The author would suggest that it 
would be well for students in their readings both 
of verse and prose, and in their classical studies as 
well as in English, to cultivate a habit of marking the 
different logical forms of discourse. It would soon 
become a pleasant pastime, as well as a profitable 
lesson. 



THE END. 



HEARS & DUSENBEEY, STEEEOTYPEES. C. SHEEMAN 4 SON, PEINTERB. 



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